Arithmetic Progression

JEE Main Mathematics · Progressions · 44 questions, latest first

• Let α=3+4+8+9+13+14+… upto 40 terms. If ( tan β)^((α)/1020) is a root of the equation x^2+x-2=0, β ∈(0, (π)/2), then sin^2 β+3…20268 April, Shift 2 · Q5
• The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P.…20266 April, Shift 1 · Q6
• Let the sum of the first n terms of an A.P. be 3 n^2+5 n. Then the sum of squares of the first 10 terms of the A.P. is:20265 April, Shift 1 · Q2
• The first term of an A.P. of 30 non-negative terms is 10/3. If the sum of this A.P. is the cube of its last term, then its common…20264 April, Shift 1 · Q7
• Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of…20262 April, Shift 1 · Q5
• The common difference of the A.P.: a_1, a_2, …, a_m is 13 more than the common difference of the A.P.: b_1, b_2, …, b_n. If…202628 January, Shift 1 · Q6
• Let a_1, a_2, a_3, a_4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If…202624 January, Shift 2 · Q5
• Consider an A.P.: a_1, a_2, …, a_n; a_1>0. If a_2-a_1=-3/4, a_n=1/4 a_1, and Σ_i=1^n a_i=525/2, then Σ_i=1^17 a_i is equal to202624 January, Shift 1 · Q6
• Let Σ_k=1^n a_k=α n^2+β n. If a_10=59 and a_6=7 a_1, then α+β is equal to202623 January, Shift 2 · Q6
• Suppose a, b, c are in A.P. and a^2, 2 b^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 ____.202622 January, Shift 2 · Q21
• 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…202622 January, Shift 1 · Q5
• Let a_n be the n^th term of an A.P. If S_n=a_1+a_2+a_3+…+a_n=700, a_6=7 and S_7=7, then a_n is equal to:20257 April, Shift 2 · Q6
• 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…20254 April, Shift 2 · Q6
• 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…20254 April, Shift 1 · Q4
• 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…20252 April, Shift 2 · Q5
• Let a_1, a_2, a_3, …. be in an A.P. such that Σ_k=1^12 a_2 k-1=-72/5 a_1, a_1 ≠ 0. If Σ_k=1^n a_k=0, then n is:20252 April, Shift 1 · Q19
• Let a_1, a_2, …, a_2024 be an Arithmetic Progression such that a_1+(a_5+a_10+a_15+…+a_2020)+a_2024=2233. Then…202529 January, Shift 2 · Q22
• 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…202529 January, Shift 1 · Q6
• 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…202528 January, Shift 2 · Q21
• Let T_r be the r^th term of an A.P. If for some m, T_m=1/25, T_25=1/20, and 20 Σ_r=1^25 T_r=13, then 5 m Σ_r=m^2 m T_r is equal to202528 January, Shift 1 · Q6
• In an arithmetic progression, if S_40=1030 and S_12=57, then S_30-S_10 is equal to:202524 January, Shift 2 · Q7
• The roots of the quadratic equation 3 x^2-p x+q=0 are 10^th and 11^th terms of an arithmetic progression with common difference…202523 January, Shift 2 · Q21
• 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,…202523 January, Shift 1 · Q6
• Suppose that the number of terms in an A.P. is 2 k, k ∈ N. If the sum of all odd terms of the A.P. is 40, the sum of all even…202522 January, Shift 2 · Q6
• An arithmetic progression is written in the following way The sum of all the terms of the 10^th row is ____.20248 April, Shift 2 · Q23
• Let the positive integers be written in the form: If the k^th row contains exactly k numbers for every natural number k, then the…20248 April, Shift 1 · Q25
• A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the…20246 April, Shift 2 · Q7
• Let a_1, a_2, a_3, … be in an arithmetic progression of positive terms. Let A_k=a_1^2-a_2^2+a_3^2-a_4^2+…+a_2 k-1^2-a_2 k^2. If…20245 April, Shift 1 · Q25
• Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7^th, 8^th and 13^th terms of an A.P. If the 5^th…20244 April, Shift 1 · Q9
• 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 the fifth…20241 February, Shift 2 · Q7
• Let 3,7,11,15, …, 403 and 2,5,8,11, …, 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to…20241 February, Shift 1 · Q25
• 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…202431 January, Shift 2 · Q7
• Let S_n denote the sum of first n terms of an arithmetic progression. If S_20=790 and S_10=145, then S_15-S_5 is:202430 January, Shift 1 · Q6
• The 20^th term from the end of the progression 20,19 1/4, 18 1/2, 17 3/4, …,-129 1/4 is:202427 January, Shift 2 · Q6
• The number of common terms in the progressions 4,9,14,19, … …, up to 25^th term and 3,6,9,12, … …, up to 37^th term is:202427 January, Shift 1 · Q7
• Let s_1, s_2, s_3, …., s_10 respectively be the sum to 12 terms of 10 A.P. s whose first terms are 1,2,3, ….., 10 and the common…202313 April, Shift 1 · Q6
• Let x_1, x_2, …, x_100 be in an arithmetic progression, with x_1=2 and their mean equal to 200. If y_i=i(x_i-i), 1 ≤ i ≤ 100,…202311 April, Shift 1 · Q13
• The sum of all those terms, of the arithmetic progression 3,8,13, …, 373, which are not divisible by 3, is equal to ____.202310 April, Shift 1 · Q26
• The sum of the common terms of the following three arithmetic progressions. 3,7,11,15, … …, 399, 2,5,8,11, … …, 359 and…20231 February, Shift 2 · Q83
• Let a_1=8, a_2, a_3, …, a_n 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…20231 February, Shift 1 · Q86
• Let a_1, a_2, a_3, … be an A.P. If a_7=3, the product a_1 a_4 is minimum and the sum of its first n terms is zero, then n!-4…202331 January, Shift 2 · Q65
• Let a, b, c>1, a^3, b^3 and c^3 be in A.P., and log_a b, log_c a and log_b c be in G.P. If the sum of first 20 terms of an A.P.,…202330 January, Shift 2 · Q67
• The 8^th common term of the series S_1=3+7+11+15+19+….., S_2=1+6+11+16+21+….. is ____.202330 January, Shift 2 · Q85
• Let A_1, A_2, A_3 be the three A.P. with the same common difference d and having their first terms as A, A+1, A+2, respectively.…202325 January, Shift 1 · Q85