Question

Sum of the series $3+7+14+24+37+....10$ terms is

• A. 560
• B. 570
• C. 580
• D. none of these

Answer 1

The correct option is B 570

Sum of the series :

Which is equal to $3$

$\Rightarrow$ term are in the form $a{x}^2+bn+c$

$\Rightarrow$ If $n=1$

$a+b+c=3$--------- $\left(1\right)$

$4a+2b+c=7$-----$\left(2\right)$

$9a+3b+c=14$----$\left(3\right)$

From $\left(1\right)$ & $\left(2\right)$

$3a+b=4$ ---- $\left(4\right)$

$5a+b=7$ ---- $\left(5\right)$

From $\left(4\right)$ & $\left(5\right)$

$2a=3$

$a=3/2$

$b=-1/2$

$c=2$

$\Rightarrow {\sum }_{k=1}^{10}\frac{3}{2}{k}^2=-\frac{1}{2}k+2$

$\frac{3}{2}\frac{\left(m\right)(n+1)(2n+1)}{6}-\frac{1}{2}\frac{\left(x\right)(x+1)}{2}+2m,$ (where $n=x$)

$\Rightarrow 560+10=570$