Question

the sun of first 16 terms of an AP is 112 and the sun of the next fourteen terms of an AP is 518. Find the AP

Answer 1

S16=112

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

let the values, n=16

S16=16/2[2a+(16-1)d]=112

=8[2a+15d]=112   =2a+15d=14 -------- 1 eq.

S16+sum of next 14 term

=S16+S14=112+518

=S30=630

S30=30/2[2a+(30-1)d]=630 .   {put the formula of Sn}

2a+22d=42 -------- 2 eq.

now, adding both the eq.1 and 2

2a+22d=42

2a+15d=14 .     {all the sign of the digit change}

14d=28 .    d=2

put the value of d in any  eq.

then the value of a we get is -8.