Question

(v) The next term of the AP √2, √8, √18,.....will be
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Answer 1

Answer:

√2.........

is the the answer.....

Answer 2

Solution:-

we may write given term as

$\sqrt{2} \: \: \: \: \: \: \: \sqrt{2 \times 4} \: \: \:\: \: \: \: \sqrt{2 \times 9}$

now we can write as

$\sqrt{2} \: \: \: \: \: \: \: \: \: 2 \sqrt{2} \: \: \: \: \: \: \: 3 \sqrt{2}$

clearly :- first find comman difference (a2-a1),we get

$2 \sqrt{2} - \sqrt{2} = 3 \sqrt{2} - 2 \sqrt{2} = \sqrt{2}$

so, the given progression is an AP with common difference

$\sqrt{2}$

next term is:-

$4 \sqrt{2} = \sqrt{16 \times 2} = \sqrt{32}$

Answer:- next term is

$\sqrt{32}$