Sequence and Series questions
1035 published questions with worked solutions.
- If the sum of an infinite geometric series is 3 and the sum of the cubes of its terms is 27 19 , then find the first term of the...
- Let a_1,a_2,a_3, be the terms of an A.P. If a_1+a_2+ +a_p a_1+a_2+ +a_q = p^2 q^2 , p q and a_6 a_ 21 = mn, where G.C.D. (m,n)=1,...
- Find the value of _ r=1 ^ (4r+5)5^ -r r(5r+5) .
- If 11 A.M.'s are inserted between 28 and 10, then find the number of integral A.M.'s.
- Let a_1,a_2,a_3, be in A.P. and g_1,g_2,g_3, be in G.P. If a_1=g_1=3 and a_8=g_4=24, then find g_7 a_4 .
- For three positive integers p,q,r, x^ pq^2 =y^ qr =z^ p^2r and r=pq+1 such that 3,3 _yx,3 _zy,7 _xz are in A.P. with common...
- If a_n= -2 4n^2-16n+15 , then a_1+a_2+ +a_ 25 is equal to
- The sum of the first 20 terms of the series 5+11+19+29+41+ , is
- Let S_K= 1+2+ +K K and _ j=1 ^nS_j^2= nA (Bn^2+Cn+D ), where A,B,C,D N and A has least value. Then
- Let a_n be the n^ th term of the series 5+8+14+23+35+50+ and S_n= _ K=1 ^na_K. Then a_1,a_2, ,a_n is equal to
- Let the positive integers a and r be the first term and common ratio of a geometric progression. If the sum of squares of its...
- Let s_1,s_2,s_3, ,s_ 10 respectively be the sum of 12 terms of 10 A.P.'s whose first terms are 1,2,3, ,10 and the common...
- Let be a G.P. of increasing positive numbers. Let the sum of its G_2^2=243 3 and G_2= 243 3 =27 terms be 2 and the product of its...
- Let A_1 and A_2 be two arithmetic means and G_1,G_2,G_3 be three geometric means of two distinct positive numbers. Then...
- Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, 3N ,N+2 are in geometric...
- If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common...
- Let x^2=4 and a=x^4=16 be in A.P., and x^4=4x^2, x^2=4 and a=x^4=16 be in G.P. If the sum of first 20 terms of an A.P., whose...
- Let S= _ r=1 ^ 10 ((r+3)!-(r+1)!-8 ((r+1)!-r! ) ) be an A.P. If _ r=1 ^ 10 ((r+3)!-(r+1)! )-8 _ r=1 ^ 10 ((r+1)!-r! ), the...
- Let (2^x-4 ) (2^x-8 )=0 be the x=2 or 3 term of an A.P. If x=2 and x=3, then the common difference of the A.P. is
- If 100 times the 100^ th term of an A.P. with non-zero common difference equals 50 times its 50^ th term, then the 150^ th term...
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