Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
i. `sqrt(2),\ 3sqrt(2),\ 5sqrt(2),\ 7sqrt(2) .......` ii. `9,7,5,3....`

Explanation

(i) `√2,3√2,5√2,7√2……`

`a_1`=√2, `a_2`=3√2, `a_3`=5√2,` a_4``=7√2`

⇒`a_4`−`a_3`=`a_3`−`a_2`=`a_2`−`a_1``=2√2`

∴ The common difference is 2√2 and the givensequence is A.P.

`a_5``=√2+2√2(5−1)=9√2`

`a_6``=√2+2√2(6−1)=11√2`

`a_7``=√2+2√2(7−1)=13√2`

(ii) `9,7,5,3,……`
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