Sequences and Series
If x be the AM and y,z be two GM's between two positive numbers, then xyzy3+z3 is equal to -
Connecting you to a tutor in 60 seconds.
Get answers to your doubts.
Find the sum to n terms of the sequence, 8, 88, 888, 8888 . . . .
If S1,S2,S3are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9S22=S3(1+8S1).
If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.
If an−1+bn−1an+bnis the A.M. between a and b, then find the value of n.
Show that a1,a2,…,an,…form an AP where anis defined as below : (i) an=3+4n (ii) an=9−5n. Also find the sum of the first 15 terms in each case.
How many terms of the A.P. 6, −211,−5,˙˙˙are needed to give the sum 25?
Show that 12×2+22×3++˙˙˙n2×(n+1)1×22+2×32++˙˙˙n×(n+1)2=3n+13n+5˙
If a, b, c, d are in G.P., prove that (an+bn),(bn+cn),(cn+an)are in G.P.