Question

which of the following list of number form a.p.s? if they form an ap find the common difference D and also write its next three term.

1. 3,3+root 2, 3+2root2, 3+3root 2.....

Answer 1

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1).

Yeah it's an A. P. S. which can be determined as, b-a = c - b

Now, to find the common difference (D)

B- A = C - B = D

So, D = 3 + root 2 - 3 = root 2.

So common difference (D) =
$\sqrt{2}$

It's next three terms will be,

$3 + 4 \sqrt{2} \\ \\ 3 + 5 \sqrt{2} \\ \\ 3 + 6 \sqrt{2}$

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Answer 2

◢GIVEN SERIES :-

$= > 3 ,\: \: 3 + \sqrt{2} ,\: \: 3 + 2 \sqrt{2}, \: \: 3 + 3 \sqrt{2} ..........$
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● WE KNOW THAT

● COMMEN DIFFERENCE = D

◢AND

D = [(n+1)th term - (n)th term.] ____[n≠0]

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◢THEN

● WE TAKE "n=1"

◢SO

=> D = [2nd term - 1st term]

$= > d = (3 + \sqrt{2} ) - 3 \\ \\ = > d = \sqrt{2}$
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◢NOW

● NEXT THREE TURM OF AP ARE

$= > 3 + 3\sqrt{2} + \sqrt{2} = 3 + 4 \sqrt{2} \\ \\ = > 3 + 4 \sqrt{2} + \sqrt{2} = 3 + 5 \sqrt{2} \\ \\ = > 3 + 5 \sqrt{2} + \sqrt{2} = 3 + 6 \sqrt{2}$
__________________[◢ANSWER ]

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