Sum of a GP and Infinite GP

JEE Main Mathematics · Progressions · 9 questions, latest first

• 6/(3^26)+(10 · 1)/(3^25)+(10 · 2)/(3^24)+(10 · 2^2)/(3^23)+…+(10 · 2^24)/3 is equal to:202628 January, Shift 2 · Q5
• (1/3+4/7)+(1/3^2+1/3 × 4/7+4^2/7^2)+(1/3^3+1/3^2 × 4/7+1/3 × 4^2/7^2+4^3/7^3)+… upto infinite terms, is equal to202624 January, Shift 2 · Q6
• Let 729,81,9,1, … be a sequence and P_n denote the product of the first n terms of this sequence. If 2…202624 January, Shift 1 · Q4
• Let a_1, (a_2)/2, (a_3)/2^2, …, (a_10)/2^9 be a G.P. of common ratio 1/(√2). If a_1+a_2+…+a_10=62, then a_1 is equal to:202621 January, Shift 2 · Q7
• Let a, a r, a r^2, … … be an infinite G.P. If Σ_n=0^∞ a r^n=57 and Σ_n=0^∞ a^3 r^3 n=9747, then a+18 r is equal to20249 April, Shift 2 · Q7
• Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle A B C and…20246 April, Shift 2 · Q16
• If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the…202429 January, Shift 1 · Q7
• If the sum of the series (1/2-1/3)+(1/2^2-1/(2 · 3)+1/3^2)+(1/2^3-1/(2^2 · 3)+1/(2 · 3^2)-1/3^3)+ (1/2^4-1/(2^3 · 3)+1/(2^2 ·…202315 April, Shift 1 · Q24
• Let {a_k} and {b_k}, k ∈ N, be two G.P.s with common ratios r_1 and r_2 respectively such that a_1=b_1=4 and r_1<r_2. Let…202329 January, Shift 2 · Q85