3, 3+√(2), 3+2√(2), 3+3√(2) a_2 a_1=3+√(2) 3 =√(2) a_3 a_2=3+2√(2) (a+√(2)) =√(2) d=√(2) a_5=a+4d =3+4√(2) a_6=a+5 ...

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Byju's Answer

Standard XII

Mathematics

nth Term of A.P

3,3+√2,3+2√2,...

Question

$3, 3 + \sqrt{2}, 3 + 2 \sqrt{2}, 3 + 3 \sqrt{2}, . . .$

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Solution

$3, 3 + \sqrt{2}, 3 + 2 \sqrt{2}, 3 + 3 \sqrt{2}$
$a_{2} - a_{1} = 3 + \sqrt{2} - 3$
$= \sqrt{2}$
$a_{3} - a_{2} = 3 + 2 \sqrt{2} - (a + \sqrt{2})$
$= \sqrt{2}$
$d = \sqrt{2}$
$a_{5} = a + 4 d$
$= 3 + 4 \sqrt{2}$
$a_{6} = a + 5 d$
$= 3 + 5 \sqrt{2}$
$a_{7} = a + 6 d$
$= 3 + 6 \sqrt{2}$
$∴$ Next $3$ term are :- $3 + 4 \sqrt{2}, 3 + 5 \sqrt{2}, 3 + 6 \sqrt{2}$

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Q. Is the given sequence

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form an APs? If it forms an AP, find the common difference

d

and write the next three terms.

Question 4 (v)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(v) $3, 3 + \sqrt{2}, 3 + 2 \sqrt{2}, 3 + 3 \sqrt{2}$

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3,3+√2,3+2√2,3+3√2,...

3,3+√2,3+2√2,3+3√2a2−a1=3+√2−3=√2a3−a2=3+2√2−(a+√2)=√2d=√2a5=a+4d=3+4√2a6=a+5d=3+5√2a7=a+6d=3+6√2∴ Next 3 term are :- 3+4√2,3+5√2,3+6√2

$3, 3 + \sqrt{2}, 3 + 2 \sqrt{2}, 3 + 3 \sqrt{2}, . . .$