Question

Find the tenth term of the equation of the sequence √2,√8,√18.....

Answer 1

Hey Pretty Stranger!

Given sequence in an A.P.

√2, √8, √18,.....

= √2, 2√2,3√2...

Hence,

a = √2, d = √2 and n = 10

$\because\: \sf a_{n}$ a + (n - 1) d

→ $\sf a_{10}$ = √2 + (10 - 1)√2

→ $\sf a_{10}$ = √2 + 9√2

→ $\sf a_{10}$ = 10√2

$\therefore\: \sf a_{10}$ = 200

Answer 2

Given ,

The sequence is :

√2 , √8 , √18 or √2 , 2√2 , 3√2

Here ,

First term (a) = √2

Common difference = √2

We know that , the general formula of an AP is given by

$\sf \large \fbox{ a_{n} = a + (n - 1)d }$

Thus ,

$\sf \mapsto a_{10} = \sqrt{2} + (10 - 1) \sqrt{2} \\ \\ \sf \mapsto a_{10} = \sqrt{2} + 9 \sqrt{2} \\ \\ \sf \mapsto a_{10} =10 \sqrt{2}$

$\therefore \sf \underline{The \: tenth \: term \: of \: given \: AP \: is \: 10 \sqrt{2} }$