Arithmetico-Geometric Progression

JEE Main Mathematics · Progressions · 9 questions, latest first

• If 7=5+1/7(5+α)+1/7^2(5+2 α)+1/7^3(5+3 α)+… … ….. ∞, then the value of α is:202524 January, Shift 2 · Q6
• If S(x)=(1+x)+2(1+x)^2+3(1+x)^3+⋯+60(1+x)^60, x ≠ 0, and (60)^2 S(60)=a(b)^b+b, where a, b ∈ N, then (a+b) equal to ____.20246 April, Shift 2 · Q23
• If 8=3+1/4(3+p)+1/4^2(3+2 p)+1/4^3(3+3 p)+⋯ ⋯ ∞, then the value of p is ____.202427 January, Shift 1 · Q24
• Let f(x)=Σ_k=1^10 k x^k, x ∈ R. If 2 f(2)+f^′(2)=119(2)^n+1 then n is equal to ____202313 April, Shift 2 · Q25
• For k ∈ N, if the sum of the series 1+4/k+8/k^2+13/k^3+19/k^4+… is 10, then the value of k is ____202311 April, Shift 2 · Q23
• Let S=109+108/5+107/5^2+….+2/(5^107)+1/(5^108). Then the value of (16 S-(25)^-54) is equal to ____202311 April, Shift 1 · Q25
• Suppose a_1, a_2, 2, a_3, a_4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric…202310 April, Shift 2 · Q24
• If (20)^19+2(21)(20)^18+3(21)^2(20)^17+…+20(21)^19=k(20)^19, then k is equal to ____.20236 April, Shift 2 · Q23
• Let a_1=b_1=1 and a_n=a_n-1+(n-1), b_n=b_n-1+a_n-1, ∀ n ≥ 2. If S=Σ_n=1^10 b_n/2^n and T=Σ_n=1^8 n/(2^n-1), then 2^7(2 S-T) is…202329 January, Shift 2 · Q86