How many terms are there in the A.P.?$-1, -\frac{5}{6}, -\frac{2}{3}, -\frac{1}{2}, …….., \frac{10}{3}$.

Given:

Given A.P. is $-1, -\frac{5}{6}, -\frac{2}{3}, -\frac{1}{2}, …….., \frac{10}{3}$.

To do:

We have to find the number of terms in the given A.P.

Solution:

Here,

$a_1=-1, a_2=-\frac{5}{6}, a_3=-\frac{2}{3}$

Common difference $d=a_2-a_1=-\frac{5}{6}-(-1)=-\frac{5}{6}+1=\frac{-5+1\times6}{6}=\frac{1}{6}$

Let $\frac{10}{3}$ be the nth term.

We know that,

nth term $a_n=a+(n-1)d$

Therefore,

$a_{n}=-1+(n-1)(\frac{1}{6})$

$\frac{10}{3}=-1+\frac{n-1}{6}$

$\frac{10}{3}+1=\frac{n-1}{6}$

$\frac{10+1\times3}{3}=\frac{n-1}{6}$

$2(13)=n-1$       (On cross multiplication)

$n=26+1$

$n=27$

Hence, there are 27 terms in the given A.P.     

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

18 Views

Kickstart Your Career

Get certified by completing the course

Get Started