If log3(x2−1), log3(2x2+1) and log3(6x2+3) are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is _______________.

Question

If log3​(x2−1), log3​(2x2+1) and log3​(6x2+3) are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is _______________.

Accepted Answer

AP condition: 2log3​(2x2+1)=log3​(x2−1)+log3​(6x2+3), giving (2x2+1)/(x2−1)=3, so x2=4.The first three terms become log3​3=1, log3​9=2, log3​27=3. Next three: 4+5+6=15.