Question

What is sum of 24 term of series root 2 + root 8 + root 18 +root 32 + .....?

Answer 1

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Answer 2

The sum of the series is $S_{24}=300\sqrt2$.

Step-by-step explanation:

Given : Series root 2 + root 8 + root 18 +root 32 + .....

To find : What is sum of 24 term of series ?

Solution :

The series is in arithmetic progression in which

First term is $a=\sqrt{2}$

Common difference is $d=\sqrt8-\sqrt2=\sqrt2$

The sum of A.P of n terms is given by,

$S_n=\frac{n}{2}[2a+(n-1)d]$

Substitute the value,

$S_{24}=\frac{24}{2}[2(\sqrt2)+(24-1)\sqrt2]$

$S_{24}=12[2\sqrt2+23\sqrt2]$

$S_{24}=12[25\sqrt2]$

$S_{24}=300\sqrt2$

Therefore, the sum of the series is $S_{24}=300\sqrt2$.

#Learn more

What is the sum to 'n' terms of the series:

5 + 6 + 10 + 16 + 24 + ...

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