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 a², 2b², c² are in G.P. If a < b < c and a+b+c = 1, then 9(a²+b²+c²) is equal to.

Σ_(k=1)ⁿ a_k = α n² + β n. a₁₀=59, a₆=7a₁. Find α+β.

Consider an A.P. a₁,a₂,…,aₙ; a₁>0. If a₂-a₁=-3/4, aₙ=1/4a₁, and Σ_(i=1)ⁿ aᵢ=525/2, then Σ_(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 l are integers. If a₁+a₂+a₃+a₄=48 and…

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

Let the arithmetic mean of 1/a and 1/b be 5/16, where a>2. If α is such that a,4,α,b are in A.P., then the equation α x²-ax+2(α-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,…

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 3x² - px + q = 0 are the 10^th and 11^th terms of an arithmetic progression with common difference 3/2.…

Let Sₙ = 1/2 + 1/6 + 1/12 + 1/20 + … up to n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p…

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

Let T_r be the r^th term of an A.P. If for some m, T_m = 1/25, T₂₅ = 1/20 and 20Σ_(r=1)²⁵ T_r = 13, then 5m Σ_(r=m)^2m T_r 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 + (a₅ + a₁₀ + a₁₅ + … + a₂₀₂₀) + a₂₀₂₄ = 2233. Then a₁ + a₂ + a₃ + … + a₂₀₂₄…

Let a₁, a₂, a₃, … be in an A.P. such that Σ_(k=1)¹² a_(2k-1) = -72/5a₁, a₁ ≠ 0. If Σ_(k=1)ⁿ a_k = 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…

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 log a, log b, log c are in an A.P. and log a - log 2b, log 2b - log 3c, log 3c - log 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)/(Σ S_k) < 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 the…

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, a³, b³ and c³ be in A.P., and log_b a, logₐ c and log_c b be in G.P. If the sum of the first 20 terms of an A.P., whose…

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 = 2a₇ and a₁₁ = 18, then 12 ( 1/(√a₁₀ + √a₁₁) + 1/(√a₁₁ + √a₁₂) + … + 1/(√a₁₇ + √a₁₈)) is equal to:

Let a₁, a₂, a₃, … be an A.P. If a₇ = 3, the product a₁ a₄ is minimum and the sum of its first n terms is zero, then n! - 4a_n(n+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 lim_n→∞…

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…