​​​Pls solve

Dear Student,
Please find below the solution to the asked query:

We have,GP: a1,a2,a3,...,an,...=log anlog an+1log an+2log an+3log an+4log an+5log an+6log an+7log an+8R1R1-R2,R3R3-R2=log an-log an+3log an+1-log an+4log an+2-log an+5log an+3log an+4log an+5log an+6-log an+3log an+7-log an+4log an+8-log an+5=log anan+3log an+1an+4log an+2an+5log an+3log an+4log an+5log an+6an+3log an+7an+4logan+8an+5=log arn-1arn+3-1log arn+1-1arn+4-1log arn+2-1arn+5-1log an+3log an+4log an+5log arn+6-1arn+3-1log arn+7-1arn+4-1logarn+8-1arn+5-1=log r-3log r-3log r-3log an+3log an+4log an+5log r3log r3logr3=-log r3-log r3-logr3log an+3log an+4log an+5log r3log r3logr3=-log r3log r3logr3log an+3log an+4log an+5log r3log r3logr3Since, R1 and R3 are identicalSo, =0Hence, the correct option is C.

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