Given p,q,r,s,t are in an arithmetic sequence. If p+q+r=9 and s+t=26, find the first term and the common difference of the sequence

Question

Anything helps

Answer 1

If d is the common difference, q=p+d, r=p+2d, s=p+3d, t=p+4d.

So p+q+r=p+p+d+p+2d=3p+3d=9, p+d=3, and p=3-d.

s+t=p+3d+p+4d=2p+7d=26.

Substitute p=3-d:

2(3-d)+7d=26,

6-2d+7d=26,

5d=20, so d=4 and p=3-d=-1.

So the first term is -1 and the common difference is 4:

-1, 3, 7, 11, 15