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8. Sequences and Series
easy
The first and last terms of a $G.P.$ are $a$ and $l$ respectively; $r$ being its common ratio; then the number of terms in this $G.P.$ is
A
$\frac{{\log l - \log a}}{{\log r}}$
B
$1 - \frac{{\log l - \log a}}{{\log r}}$
C
$\frac{{\log a - \log l}}{{\log r}}$
D
$1 + \frac{{\log l - \log a}}{{\log r}}$
Solution
(d) $l = a{r^{n – 1}}$ $ \Rightarrow $ $\frac{{l}}{{a}}=r^{n-1}$
$ \Rightarrow $ $1 + \frac{{\log l – \log a}}{{\log r}}=n$
Standard 11
Mathematics
