First and last terms of a G.P. are a and l respectively; r being its common ratio; then number of te

English

Gujarati

Hindi

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

Share

Similar Questions

Let ${a_1},{a_2}…,{a_{10}}$ be a $G.P.$ If $\frac{{{a_3}}}{{{a_1}}} = 25,$ then $\frac {{{a_9}}}{{{a_{ 5}}}}$ equal

hard

(JEE MAIN-2019)

If $a, b, c$ and $d$ are in $G.P.$ show that:

$\left(a^{2}+b^{2}+c^{2}\right)\left(b^{2}+c^{2}+d^{2}\right)=(a b+b c+c d)^{2}$

medium

Let $M=2^{30}-2^{15}+1$, and $M^2$ be expressed in base $2$.The number of $1$'s in this base $2$ representation of $M^2$ is

normal

(KVPY-2020)

In a geometric progression, if the ratio of the sum of first $5$ terms to the sum of their reciprocals is $49$, and the sum of the first and the third term is $35$ . Then the first term of this geometric progression is

hard

(JEE MAIN-2014)

Let $a_1, a_2, a_3, \ldots .$. be a sequence of positive integers in arithmetic progression with common difference $2$. Also, let $b_1, b_2, b_3, \ldots .$. be a sequence of positive integers in geometric progression with common ratio $2$ . If $a_1=b_1=c$, then the number of all possible values of $c$, for which the equality

$2\left(a_1+a_2+\ldots .+a_n\right)=b_1+b_2+\ldots . .+b_n$

holds for some positive integer $n$, is. . . . . . .

hard

(IIT-2020)