Question

th sum of first q terms of an ap is 162.the ratio of its 6 th term to its 13 th term is 1:2.find the first and 15th term of the ap

Answer 1

Given:sum of terms =162
Ratio of 6th term and13th trm 1:2
Formula is an=a1+(n-12)d
As given a6/a13=1/2
a1+5d / a1+12d=1/2

After cross multiplication
2 (a1+5d)=1 (a1+12d)
2a1+10d=a1+12d
2a1+a1=12d-10d
Therefore the first term a1=2d

Sn=(n/2)(2a+(n-1)d)
S9=9/2 (2 (2d)+(9-1)d)
S9=(9/2)(4d+8d)
162=9 (6d)
594=162
d=3
a1=2d=6
a15=6+(15-1)3 = 6+3 (14) = 48

Therefore 1st trem=6
And 15th trem=48

Thats it
I hope u understood
Its slightly risky
Try it again and again
Then it will be easy fr u i hope
All the best