Question

the sum of first six terms of an ap is 42 the ratio of its 10 term to 30 term is 1:3 calculate the first and 13 termof the ap

Answer 1

Sn=n/2[2a+(n-1)d]
S6=6/2[2a+(n-1)d)]
42=3(2a+5d)
2a+5d=14




A10/130=1/3
3(a10)=a(30)
3(a+9d=a+29d
3a+27d=a+29d
2a=2d
A=D




Now 2a+5a=14. ,.....because a=d
7a=14
A=2
D=2

A13=a+12d=a+12a. ......because a=d
A13=13a
A13=13(2)
Therefore
A13=26


Hope it helps...