The first term of the G.P. is $25$ and $6$ th term is $800$ . Find the seventh term.

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Solution

We can see that: $a = 25, T_{6} = 800, T_{7} = ?$
To find $T_{7}$ , we should first find r.
$T_{6} = 800$
$a r^{5} = 800$
$25 \times r^{4} = 900, r^{=} 32$
$r^{5} = 2^{5}$
$∴ r = 2$
We know that, $T_{n + 1} = T_{n} \times r$
$T_{7} = T_{6} \times r$
$T_{7} = 800 \times 2$
$∴ T_{7} = 1600$

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