Question

PLEASE HELP! SUPER IMPORTANT!
The 1st, 5th, and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence.

Answer 1

let the terms of gp be a,ar,ar^2,r=2 given,
term21 = 72
=> a+(21-1)d=72 gives a+ 20d =72,
term5=ar given
=> a+(5-1)d=2a given in question,
=>a+4d=2a gives a=4d,
put the value of d in term21 eqution which gives a =12,
use gp formula as now u will kno the terms of gp,
ans gives (12/11)*((12^10)-1)

Answer 2

thank you!

Answer 3

welcome :)