How do you find the sum of the first 18 terms of $7+(-21)+63+(-189)+...$ ?

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Answer 1 · 2016-09-13T13:29:20

Sum of first $18$ terms is $-1743392196$

As here $-21/7=63/(-21)=(-189)/63=-3$ , here we have a geometric series with first term as $7$ and common ratio as $-3$ .

As in a geometric series with first term as $a$ and common ration $r$ ,

sum of first $n$ terms is given by $(a(1-r^n))/(1-r)$

Hence, in the given series sum of first $18$ terms is given by

$(18xx(1-(-3)^18))/(1-(-3))$

= $(18xx(1-387420489))/4$

= $-(18xx387420488)/4$

= $-18xx96855122$

= $-1743392196$

How do you find the sum of the first 18 terms of 7+(-21)+63+(-189)+...7+(-21)+63+(-189)+...?