Question

The number of terms of the $A P\,\, 3,7,11,15 \ldots$ to be taken so that the sum is $210$, is :

• A. 10
• B. 12
• C. -1
• D. 2

Answer 1

Answer: (A)

Given series is $ 3,\,\,7,\,\,11,\,\,15,... $
whose first term is $ 3 $ ,
common difference $ 4 $ and sum is $ 210 $ .
Let n be the number of term.
$ \therefore $ $ S=\frac{n}{2}[2a+(n-1)d] $
$ \Rightarrow $ $ 210=\frac{n}{2}[6+(n-1)4] $
$ \Rightarrow $ $ 210=n[3+2n-2] $
$ \Rightarrow $ $ 2n^{2}+n-210=0 $
$ \Rightarrow $ $ n=10 $