Question

if the 8th term of an ap is the geometric mean of first and 22nd terms of the same find the common difference of the AP given that the sum of the first and 22 terms of the ap is 770​

Answer 1

Step-by-step explanation:

A-7d =(A*(A-21d))1/2 implies that,A2+49d2-14dA=A2-21dA,

or 49d2+7dA=0,or A= -7d .........(1)

now. sum of first 22 terms

=n/2(2a-21d)=770

from eq 1 putting the value of d,we get

n/2(2A+21×A/7)=770

=22/2(5A)=770

implies that A=14

which gives d= -2