The sum to n terms of the sequence  log⁡a,log⁡ar,log⁡ar2,… is

The given sequence can be expressed aslog⁡a,(log⁡a+log⁡r),(log⁡a+2log⁡r)…which is clearly an A.P. whose first term is log a and common difference is log r.The nth term =log⁡a+(n−1)log⁡rSince sum to n terms s=n2a1+an∴ Sn=n2[log⁡a+log⁡a+(n−1)log⁡r]=n2[2log⁡a+(n−1)log⁡r]=n2log⁡a2rn−1