Sequences and Series — MATHS STD 11 Science — Question

1. 2870

Solution:

Given,

$\sum\text{n}=210$

$\Rightarrow\text{n}\Big(\frac{\text{n}+1}{2}\Big)=210$

$\Rightarrow\text{n}^2+\text{n}-420=0$

$\Rightarrow(\text{n}-20)(\text{n}+21)=0$

$\Rightarrow\text{n}=20$ $(\because\ \text{n}>0)$

Now,

$\sum\text{n}^2=\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}$

$\Rightarrow\frac{\text{n}(\text{n}+1)}{2}\times\frac{(2\text{n}+1)}{3}$

$\Rightarrow(210)\times\Big(\frac{41}{3}\Big)$

$\Rightarrow(70)\times(41)$

$\Rightarrow2870$