S 1+s7=2(s4-s3) 1 and s2+s8=2(s5-s3).

Subtract the two expressions to get A2+a8=2a5.

An is arithmetic progression, that is, an= 1+(n- 1)d,

Then s2+s8=2(s5+s3), and s 1+s9=2(s5+s4).

Subtract the two expressions to get a9-a2=2a4.

That is, 7d=2+6d.

So d=2

an=2n- 1