Arithmetic Progression — nth term + Sum
Sequences & Series
60
JEE Qs
6%
Hard
75
min
Master the direct application of AP formulas and practice strategic selection of terms to simplify problem-solving, especially when sums or products of terms are involved.
🧮 Key Formulas
✅ Key Points for JEE
- 1An Arithmetic Progression (AP) is characterized by a constant common difference 'd' between consecutive terms.
- 2For problems involving sums or products of a small number of terms in AP, strategically select terms like (a-d, a, a+d) for 3 terms, or (a-3d, a-d, a+d, a+3d) for 4 terms, to simplify calculations.
- 3The nth term (a_n) of an AP is a linear function of 'n', i.e., of the form An + B.
- 4The sum of n terms (S_n) of an AP is a quadratic function of 'n' without a constant term, i.e., of the form An^2 + Bn.
- 5If the sum of n terms (S_n) is given, the nth term can be found using the relation a_n = S_n - S_{n-1} for n > 1, and a_1 = S_1.
⚠️ Common Mistakes
- ✕Incorrectly using 'n' instead of '(n-1)' in the nth term or sum formulas, leading to 'off-by-one' errors.
- ✕Errors in identifying the first term 'a' or common difference 'd', especially in word problems or when terms are not explicitly given from the start.
- ✕Confusing the nth term (a_n) with the sum of n terms (S_n), or applying the wrong formula for the required quantity.
📝 Practice Questions
See allQ12.The remainder, when 7103 is divided by 23 , is equal to : (1) 6 (2) 17 (3) 9 (4) 14
Q22.Let a1, a2, … , a2024 be an Arithmetic Progression such that a1 + (a5 + a10 + a15 + … + a2020) + a2024 = 2233. Then a1 + a2 + a3 + … + a2024 is equal to _______ 1 2 3 , then α is equal to ________ (3x + t = 5eα ( 85 )
Q1. Let a1, a2, a3, … be a G.P. of increasing positive terms. If a1a5 = 28 and a2 + a4 = 29, then a6 is equal to: (1) 628 (2) 812 (3) 526 (4) 784 = 0. If x(1) = 1, then x ( 12 ) is :
Q15.If ∑nr=1 Tr = (2n−1)(2n+1)(2n+3)(2n+5)64 , then limn→∞∑nr=1 ( Tr1 ) (1) 0 (2) 23 (3) 1 (4) 13
Q13.Suppose that the number of terms in an A.P. is 2k, k ∈N . If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to : (1) 6 (2) 5 (3) 8 (4) 4 y+2
Q1. If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to (1) −1080 (2) −1020 (3) −1200 (4) −120
NCERT Chapters
- Class 11 Mathematics Ch 9: Sequences and Series