Question

S=29+36+43+.....+169=

Answer 1

$\displaystyle 29+36+43+...+169 \\ \\ 169=29+(n-1) \times 7 \\ \\ 169=29+7n-7 \\ \\ 7n=169-29+7 \\ \\ 7n=147 \\ \\ n= \frac{147}{7} \\ \\ n=21$

$\displaystyle S_{21}= \frac{58+20 \times 7}{2} \times 21 \\ \\ S_{21}= \frac{58+140}{2} \times 21 \\ \\ S_{21}= \frac{198}{2} \times 21 \\ \\ S_{21}=99 \times 21 \\ \\ S_{21}=2079$