The sum of first four terms of the G.P. 2, 6, 18, ........., is : 1. 26 2. 80 3. 160 4. 52

By formula, Common ratio = r = = 3. By formula, ⇒ a n = ar n - 1 ⇒ a 4 = 2 × (3) 4 - 1 ⇒ a 4 = 2 × 3 3 ⇒ a 4 = 2 × 27 = 54. Sum of first four terms of G.P. = 2 + 6 + 18 + 54 = 80. Hence, Option 2 is the correct option.

Mathematics

The sum of first four terms of the G.P. 2, 6, 18, ………, is :
26
80
160
52

AP GP

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Answer

By formula,

Common ratio = $\dfrac{a$

r = $\dfrac{6}{2}$ = 3.

By formula,

⇒ a_n = ar^{n - 1}

⇒ a₄ = 2 × (3)^{4 - 1}

⇒ a₄ = 2 × 3³

⇒ a₄ = 2 × 27 = 54.

Sum of first four terms of G.P. = 2 + 6 + 18 + 54 = 80.

Hence, Option 2 is the correct option.

Answered By

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Mathematics

The sum of first four terms of the G.P. 2, 6, 18, ………, is :
26
80
160
52

AP GP

Answer

Related Questions

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Mathematics

The sum of first four terms of the G.P. 2, 6, 18, ………, is :268016052

AP GP

Answer

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The sum of first four terms of the G.P. 2, 6, 18, ………, is :
26
80
160
52

If a, b and c are in G.P. and a, x, b, y, c are in A.P. prove that :
(i) $\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{2}{b}$
(ii) $\dfrac{a}{x} + \dfrac{c}{y} = 2.$

The 4^th term of a G.P. is 54 and its 7^th term is 1458, the common ratio of this G.P. is :
$\dfrac{1}{3}$
3
-3
$-\dfrac{1}{3}$

The geometric mean between 8 and 32 is :
24
256
40
16