Number Series (AP & GP) Tests — Pick a Level and Start
Tap a level to see every test in it. Start at Level 1 the day the formulas are learnt, then move to Level 2 with the timer running to push accuracy under pressure.
Level 1 Basic Checking… View tests
One formula applied cleanly — the 21st term of an AP, the sum of the first twenty terms, how many terms a finite list holds, the sum of the multiples of 7 in a range, a geometric mean, and the sum to infinity of a shrinking GP. Attempt these without the clock while the formulas are still fresh.
Level 2 Tier I Standard Checking… View tests
Real SSC CGL Tier I difficulty — two ideas chained in one question: a term relation combined with a known term, two blocks of ten summed separately, the ratio of two sums converted into a ratio of terms, numbers divisible by 7 but not 3, three AP terms that also form a GP, and a GP whose infinite sum is given alongside the infinite sum of its squares. This is the score that tells you the chapter is exam-ready.
Number series built on arithmetic and geometric progressions is one of the safest scorers in the SSC CGL Quantitative Aptitude paper. A shift almost always carries a question that belongs to it outright — a term of an AP, the total of a finite list, the sum of every multiple of a number inside a range, or three numbers whose sum and product are given — and the same formulas decide how fast you get through the standard sums of squares and cubes that turn up inside simplification.
These practice tests put twenty-five series questions in front of you in one sitting, which is what turns the formulas from something you can recite into something you apply without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.
How Many Series (AP & GP) Questions Are Asked in SSC CGL?
The chapter usually gets one to two direct questions, and its formulas are reused inside simplification and the standard-series questions that appear across the arithmetic block.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Number Series (AP & GP) | 1–2 | 1–2 |
| Simplification | 1–2 | 2–3 |
| Number System | 2–3 | 3–4 |
| Algebra | 2–3 | 3–4 |
| Square & Cube Roots | 1 | 1–2 |
Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.
What You Will Practice in the Series (AP & GP) Chapter
Core topics
- Telling an AP from a GP from an HP, and reading the type off a general term
- The nth term of an AP, the position of a value, and the first term to cross a bound
- Counting the terms of a finite list, and the positive or negative terms of a falling one
- The sum of an AP in both forms, and finding the count when the total is given
- Terms and blocks pulled out of a sum written as a formula in n
- Recovering the first term and common difference from two conditions
- Sums of naturals, odds, evens and multiples inside a range, including two conditions at once
- Three, four and five numbers in AP through the symmetric forms
- Arithmetic means, and inserting means between two numbers
- Index results — equidistant terms, the middle term, block sums, Sm = Sn
- Comparing two APs by their sums or their terms
- The nth term and sum of a GP, finite and to infinity
- Geometric means, three numbers in GP, and products of terms
- Growth, decay, bouncing balls and recurring decimals as geometric progressions
- AP and GP together, AM–GM–HM, and harmonic progression
- Sums of squares and cubes, and their stretched, even and alternating variations
Formulas you must know cold
| Situation | Formula | Example |
|---|---|---|
| nth term of an AP | an = a + (n − 1)d | 7, 12, 17, … → a21 = 7 + 20×5 = 107 |
| Number of terms | n = (l − a)/d + 1 | 8, 13, …, 253 → 50 terms |
| Sum of an AP | n/2 [2a + (n − 1)d] = n/2 (a + l) | 4, 9, 14, … 20 terms → 1030 |
| Term from a sum formula | an = Sn − Sn−1 | Sn = 3n2+5n → a8 = 50 |
| nth term of a GP | tn = a rn−1 | 3, 6, 12, … → t8 = 384 |
| Sum of a GP | a(rn − 1)/(r − 1) | 5, 10, 20, … 7 terms → 635 |
| Sum to infinity | a/(1 − r), only for |r| < 1 | 9, 3, 1, … → 27/2 |
| Σn, Σn2, Σn3 | n(n+1)/2, n(n+1)(2n+1)/6, [n(n+1)/2]2 | to 20 → 210, 2870, 44100 |
The multiplier is (n − 1) in both term formulas, because reaching the first term takes no steps at all. Inside a GP sum the exponent is n itself — mixing the two is the classic error of this chapter.
Symmetric forms that collapse the algebra
| Numbers | Write them as | What collapses |
|---|---|---|
| Three in AP | a − d, a, a + d | Sum = 3a; sum of squares = 3a2 + 2d2 |
| Four in AP | a − 3d, a − d, a + d, a + 3d | Sum = 4a; the real step is 2d |
| Three in GP | a/r, a, ar | Product = a3, so a is its cube root |
| Three in AP condition | 2y = x + z | Turns any "in AP" statement into one equation |
| Three in GP condition | y2 = xz | Turns any "in GP" statement into one equation |
Index results that skip the working
- Equal index sums: if p + q = r + s then ap + aq = ar + as; terms equidistant from the ends always add to a + l.
- Middle term: for an odd count Sn = n × middle term; for an even count Sn = n/2 × the middle pair.
- Swapped index and value: ap = q with aq = p gives ap+q = 0; and Sm = Sn gives Sm+n = 0.
- Sums to terms: put n = 2m − 1 into a ratio of sums to get the ratio of the mth terms.
- GP products: p + q = u + v gives tptq = tutv; the product of an odd number of GP terms is the middle term to that power.
Also worth memorising
- Sum of the first n odd numbers = n2; of the first n even numbers = n(n + 1)
- Sn = An2 + Bn is always an AP with d = 2A and first term A + B
- k arithmetic means: d = (l − a)/(k + 1), and the mth mean is a + md — not a + (m − 1)d
- k geometric means: rk+1 = l/a, and the mth mean is a rm
- AM ≥ GM ≥ HM, with GM2 = AM × HM, and (x − y)2 = 4(AM2 − GM2)
- Nested GP sums: S2n/Sn = 1 + rn. Side-by-side blocks: next n / first n = rn
- Σn2 to 10 = 385 and to 20 = 2870; Σn3 to 12 = 6084
Solved Examples — SSC CGL Number Series (AP & GP)
How the Series (AP & GP) Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the formulas.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Series (AP & GP) for SSC CGL
- Learn the four core formulas before anything else. The nth term and sum of an AP, and the nth term and sum of a GP, carry most of the chapter on their own.
- Say "one step fewer" every time. Both term formulas carry n − 1, and getting that wrong shifts the answer by exactly one term — which is always among the options.
- Use the symmetric forms whenever three or four numbers are described. a − d, a, a + d for an AP and a/r, a, ar for a GP turn a two-unknown problem into a one-line one.
- Learn the index results as a family. Equal index sums, the middle term and Sm = Sn solve the questions where a and d cannot be found at all.
- Check |r| < 1 before writing an infinite sum. If the ratio is 1 or more in size, the sum does not exist and the question is asking something else.
- Test every root against the words of the question. A quadratic in n often has two roots, and "positive", "increasing" or a row that cannot hold negative trees is what picks between them.
- Do Level 1 untimed, the same day you finish the formulas. The aim is correct recall, not speed.
- Move to Level 2 with the 30-minute clock on. A term or sum that takes more than twenty seconds means you are still deriving the formula instead of applying it.
- Study it with the standard sums. Do number system before, and keep Σn2 and Σn3 at hand for simplification.
- Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.
Series (AP & GP) Study Notes
Every formula used in these tests is explained from zero in the chapter notes — what each rule says, why it is shaped that way, and the mistake it usually costs. Read a section, then attempt the matching level here.
SSC CGL श्रेढ़ी (Number Series — AP & GP) चैप्टर टेस्ट — हिंदी में
श्रेढ़ी SSC CGL गणित का एक स्थिर अंक देने वाला अध्याय है। लगभग हर शिफ्ट में इसका 1–2 प्रश्न सीधे आता है — जैसे समान्तर श्रेढ़ी का कोई पद, किसी सीमित सूची का योग, किसी परिसर के भीतर गुणजों का योग, या ऐसी तीन संख्याएँ जिनका योग और गुणनफल दिया हो — और यही सूत्र वर्गों तथा घनों के मानक योगों में भी काम आते हैं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 30 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।
याद रखने योग्य सूत्र: AP का nवाँ पद a + (n − 1)d और योग n/2 [2a + (n − 1)d] = n/2 (a + l); GP का nवाँ पद a rn−1 और योग a(rn − 1)/(r − 1); तथा अनन्त तक योग a/(1 − r), जो केवल |r| < 1 पर ही होता है। AP की तीन संख्याएँ a − d, a, a + d लीजिए और GP की तीन a/r, a, ar — इससे योग या गुणनफल तुरन्त सिमट जाता है।
पूरे अध्याय के नोट्स हिंदी में यहाँ पढ़ें: श्रेढ़ी (AP और GP) — सम्पूर्ण स्टडी नोट्स।