Let a be the first term and r be the common ratio of the G.P.
∴ a = -3
It is known that, an = \(arn^-1\)
∴\(a^4\) = a\(r^3\)= (-3) \(r^3\)
\(a^2\) = a \(r^1\)= (-3) r
According to the given condition,
(-3) \(r^3\) = [(-3) r\(]^2\)
⇒ -3\(r^3\)= 9 \(r^2\)
⇒ r = -3
\(a^7\) = a\(r^7-1\)
= a \(r^6\)
= (-3) (-3\()^6\)
= - (3\()^7\)
= -2187
Thus, the seventh term of the G.P. is -2187.
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take sb on: | to employ sb; to engage sb to accept sb as one’s opponent in a game, contest or conflict |
take sb/sth on: | to decide to do sth; to allow sth/sb to enter e.g. a bus, plane or ship; to take sth/sb on board |