Question

The sum of first 7 terms of an ap is 182

Answer 1

Step-by-step explanation:

Let a be the first term and d be the common difference.

ATQ

(a4=a+3d)/(a7=a+6d)=1/5

5a+15d=a+16d

4a=d. eq1

It is given that

Sn=n/2(2a+(n-1)d)

=7/2(2a+6d)=182

=7(a+3d)=182

=a+3d=26.....eq2

By substitution method:-

a+3(4a)=26

13a=26

a=2

put in eq 1

4a=d

8=d

Therefore ap:-

a=2

a+d=2+8=10

a+2d=2+16=18

2,10,18............