Question

the sum of 2nd and 7th is 30 , if the 13th term is one less than twice it's 8th term , find A.P.

Answer 1

let the AP be   a,a+d,a+2d............a+(n-1)d

T2= a+d      T7=a+6d

a+d+a+6d=30 ,  2a+7d=30.............(1)

T13=a+12d ,  T8=a+7d

T13=2(T8)-1

a+12d=2a+14d-1

a+2d=1..................(2)

a=1-2d  subsitute the value of a in eq(1)

2(1-2d)+7d=30

2-4d+7d=30        

d=4

a= 1-2(4)

a=-7

AP=  -7,-3,1............