Question

Find the sum of first 25 terms of an A.P. whose $n^{th}$ term is given by $T_n=(7-3n)$

• A. 800
• B. -803
• C. 735
• D. None of these

Answer 1

The correct option is D None of these

Given, $T_n=7-3n$.

Let us try to reaarange it into the form, $T_n=a+(n-1)d$

where $a$ is the first term,$n$ is the number of terms and $d$ is the common difference.

$T_n=7-3n$

$\Rightarrow$ $T_n=4+3-3n$

$\Rightarrow$ $T_n=4-3(n-1)$

So,here $a=4,d=-3$

Sum of $n$ terms in an AP can be calculated using the formula

$S_n=\frac{n}{2}(a+T_n)$

$\Rightarrow$ $S_n=\frac{n}{2}(4+7-3n)$

$\Rightarrow$ $S_n=\frac{n}{2}(11-3n)$

$\Rightarrow$ $S_n=\frac{25}{2}(-64)$ ($\because n=25$)

$\Rightarrow$ $S_n=-800$

$\therefore$ No Option