Question

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

• A. $27$
• B. $18$
• C. $16$
• D. $9$

Answer 1

Answer: (A)

$27$

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

Here, first term $\left(a\right)=-1$ and the common difference $\left(d\right)=\frac{-5}{6}-(-1)=\frac{1}{6}.$
Let $n$ be the number of terms of the given A.P.

We know that the $n_{th}$ term of an A.P. is:

$a_n=a+(n-1)d$
Here, $a_n=\frac{10}{3}$

$\therefore a+(n-1)d=\frac{10}{3}$

$\Rightarrow -1+(n-1)\times \frac{1}{6}=\frac{10}{3}$

$\Rightarrow (n-1)\times \frac{1}{6}=\frac{13}{3}$

$\Rightarrow n-1=26$

$\Rightarrow n=27$

Therefore, there are $27$ terms in the give A.P.