Arithmetic Progression (AP): JEE Questions & Solutions

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

Suppose a, b, c are in A.P. and a^2, 2b^2, c^2 are in G.P. If a < b < c and a+b+c = 1, then 9(a^2+b^2+c^2) is equal to.

k=1^n ak = n^2 + n. a10=59, a6=7a1. Find +.

Consider an A.P. a1,a2,,an; a10. If a2-a1=- 34, an= 14a1, and i=1^n ai= 5252, then i=1^17 ai is equal to

Let a1,a2,a3,a4 be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If a1+a2+a3+a4=48 and…

The common difference of the A.P.: a1, a2,, am is 13 more than the common difference of the A.P.: b1, b2,, bn. If b31 = -277, b43 = -385…

Let the arithmetic mean of 1a and 1b be 516, where a2. If a,4,b are in A.P., then the equation ax^2-ax+2(a-2b)=0 has:

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…

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…

The roots of the quadratic equation 3x^2 - px + q = 0 are the 10^ th and 11^ th terms of an arithmetic progression with common difference…

Let Sn = 12 + 16 + 112 + 120 + up to n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is…

In an arithmetic progression, if S40 = 1030 and S12 = 57, then S30 - S10 is equal to:

Let Tr be the r^th term of an A.P. If for some m, Tm = 125, T25 = 120, and r=1^25 Tr = 13, then 5m r=m^2m Tr is equal to:

The interior angles of a polygon with n sides, are in an A.P. with common difference 6^. If the largest interior angle of the polygon is…

Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and…

Let a1, a2,, a2024 be an Arithmetic Progression such that a1 + (a1 + a0 + a1 + a2 + + a2020 + a2024) = 2233. Then a1 + a2 + a3 + + a2022 is…

Let a1, a2, a3, be in an A.P. such that k=1^12 2a2k - 1 = 725, and k=1^n ak = 0, then n is:

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds…

Let A = 1, 6, 11, 16, and B = 9, 16, 23, 30, be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A B) is

Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p,…

Let an be the n-th term of an A.P. If Sn = a1 + a2 + a3 + + an = 700, a6 = 7, and S7 = 7, then an is equal to:

Number of common terms in sequences 4, 9, 14... up to 25th term and 3, 6, 9... up to 37th term:

The 20^ th term from the end of the progression 20, 19.25, 18.5, 17.75,, -129.25 is:

In an A.P., the sixth term a6 = 2. If the product a1 a4 a5 is maximized, the common difference of the A.P. is equal to:

If a, b, c are in an A.P. and a - 2b, 2b - 3c, 3c - a are also in an A.P., then a: b: c is equal to:

Let Sn denote the sum of the first n terms in an arithmetic progression. If S20 = 790 and S10 = 145, then S15 - S5 is:

Let Sn be the sum of the first n terms of an arithmetic progression 3, 7, 11,. If n(n + 1) Sk < 42, then n equals:

Let 2^ nd, 8^ th, and 44^ th terms of a non-constant A.P. be respectively the 1^ st, 2^ nd, and 3^ rd terms of a G.P. If the first term of…

Let S(n) denote the sum of the first n terms of an arithmetic progression. If S(10) = 390 and the ratio of the tenth and fifth terms is…

Let three real numbers a, b, c be in arithmetic progression, and a + 1, b, c + 3 in geometric progression. If a 10 and their arithmetic…

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of…

Let A1, A2, A3 be the three A.P. with the same common difference d and having their first terms as A, A+1, A+2, respectively. Let a, b, c…

Let a, b, c 1, a^3, b^3 and c^3 be in A.P., and b a, a c and c b be in G.P. If the sum of the first 20 terms of an A.P., whose first term…

The 8th common term of the series S1 = 3 + 7 + 11 + 15 + 19 +, S2 = 1 + 6 + 11 + 16 + 21 +, is

Let a1, a2,, an be in A.P. If a5 = 2a1 and a1 = 18, then 12 ( 1 a0 + a1 + 1 a1 + a2 + + 1 a17 + a18) is equal to:

Let a1, a2, a3, be an A.P. If a4 = 3, the product a1 a4 is minimum and the sum of its first n terms is zero, then n! - 4an(an+2) is equal…

Let a1 = 8, a2, a3, an be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170, then the product of…

The sum of the common terms of the following three arithmetic progressions: - 3, 7, 11, 15,, 399, - 2, 5, 8, 11,, 359, - 2, 7, 12, 17,,…

Let a1, a2, a3,..., an be n positive consecutive terms of an arithmetic progression. If d 0 is its common difference, then: n ( 1 n) ( 1…

The sum of all terms of the arithmetic progression 3, 8, 13,..., 373, which are not divisible by 3, is:

Let s1, s2, s3,, s10 respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1, 2, 3,, 10 and the common differences are 1,…