Question

4,11,21,34….. Find the value of $\frac{(S_{29}-S_{9})}{60}$?

Answer 1

The correct answer is 223
$S=4+11+21+34+ ........ +T_n$
$S= \quad4+11+21+.....+Tn-1+Tn\\\\\overline{\quad Tn=4+7+10+13+.....+(Tn+Tn-1)}$
$T_n=4+\frac{(n-1)}{2} [ 14+(n-2)3]$
$\quad\ =4+\frac{(n-1)}{2} [8+3n]$
$T_n=4+\frac{1}{2} (3n^2+5n-8)$
$∑T_n = S_n=\frac{3}{2}∑n^2 + \frac{5}{2}∑n$
$\quad\quad\ \ =\frac{3}{2} \frac{n(n+1)(2n+1)}{6} + \frac{5}{2} \frac{n(n+1)}{2}$
$\quad\quad\ \ \ \frac{S_{29} - S_{9}}{60} = 223$