7th term of the sequence -2-10-5-2- is

Given sequence √(2),√(10),√(50),......... is a G.P Common ratio, r = √(10)/√(2) =√(5), First term a = √(2). Then 7^th nbsp;term, t_7 = √(2)(√(5))^7 1 = nbs ...

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Byju's Answer

Standard XI

Mathematics

nth Term of GP

7th term of t...

Question

$7^{t h}$ term of the sequence $\sqrt{2}, \sqrt{10}, 5 \sqrt{2}, . . . . . . . . .$ is

$125 \sqrt{10}$

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$25 \sqrt{2}$

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125

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$125 \sqrt{2}$

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Solution

The correct option is D
$125 \sqrt{2}$

Given sequence $\sqrt{2}, \sqrt{10}, \sqrt{50}, . . . . . . . . .$ is a G.P
Common ratio, r = $\frac{\sqrt{10}}{\sqrt{2}}$ = $\sqrt{5}$ , First term a = $\sqrt{2}$ .
Then $7^{t h}$ term,

$t_{7}$ = $\sqrt{2} (\sqrt{5})^{7 - 1}$ = $\sqrt{2} (\sqrt{5})^{6}$ = $\sqrt{2} (5)^{3}$ = 125 $\sqrt{2}$

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7th term of the sequence √2,√10,5√2,......... is

The correct option is D 125√2 Given sequence √2,√10,√50,......... is a G.P Common ratio, r = √10√2 =√5, First term a = √2. Then 7th term, t7 = √2(√5)7−1 = √2(√5)6 = √2(5)3 = 125√2

$7^{t h}$ term of the sequence $\sqrt{2}, \sqrt{10}, 5 \sqrt{2}, . . . . . . . . .$ is