<PRE><B>Question 758581</B>
Q:
In a geometric series, {{{t[1]}}} = 3 and {{{S[3]}}} = 21. Find the common ratio and the sum of the first 7 terms.
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A:
3 + 3r + {{{3r^2}}} = 21
1 + r + {{{r^2}}} = 7
{{{r^2}}} + r - 6 = 0
(r + 3)(r - 2) = 0
r = 2 OR -3
The common ratio, r is {{{highlight(2)}}} or {{{highlight(-3)}}}.
If the common ratio is 2, then the sum of the first 7 terms is:
3 + 6 + 12 + 24 + 48 + 96 + 192 = {{{highlight(381)}}}.
If the common ratio is -3, then the sum of the first 7 terms is:
3 + (-9) + 27 + (-81) + 243 + (-729) + 2187 = {{{highlight(1641)}}}</PRE>