Question

In an A.P. $t_{26}=51$ then sum of its first $51$ terms is:

• A. $2500$
• B. $2601$
• C. $2551$
• D. $2401$

Answer 1

Answer: (B)

$2601$

Since, $t_{26}=a+25d=51$ …………$\left(1\right)$

$S_{51}=\frac{51}{2}[2a+(n-1\left)d\right]$

$=\frac{51}{2}[2a+50d]$

$=51[a+25d]$ (from equation $\left(1\right)$)

$=51\times 51$

$=2601$.