(C) The given series is a geometric progression $(GP)$.Here,the first term $a = \frac{1}{4}$.The common ratio $r = \frac{-1/2}{1/4} = -2$.The formula

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(C) The given series is a geometric progression $(GP)$.Here,the first term $a = \frac{1}{4}$.The common ratio $r = \frac{-1/2}{1/4} = -2$.The formula for the $n^{th}$ term of a $GP$ is $a_n = a \cdot r^{n-1}$.To find the $5^{th}$ term $(n = 5)$:$a_5 = \frac{1}{4} \times (-2)^{5-1}$$a_5 = \frac{1}{4} \times (-2)^4$$a_5 = \frac{1}{4} \times 16$$a_5 = 4$.

Competitive Quantitative Aptitude Progression and Sequence Progression and Sequence

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Write down the $5^{th}$ term of the series $\frac{1}{4} - \frac{1}{2} + 1 \ldots$

A
$6$
B
$8$
C
$4$
D
$10$

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Progression and Sequence

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Progression and Sequence

If $a, b, c$ are positive integers,then $(a + b)(b + c)(c + a)$ is

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Find the sum of all integers between $50$ and $500$ which are divisible by $7.$

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The sum of three numbers in a $GP$ is $105$ and their product is $8000$. Find the numbers.

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If the sum of $n$ terms of a $G.P.$ is $255$,the $n^{th}$ term is $128$,and the common ratio is $2$,then the first term will be:

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The solution of the equation $1 + a + a^2 + a^3 + \dots + a^x = (1 + a)(1 + a^2)(1 + a^4)$ is given by $x$ is equal to

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Write down the $5^{th}$ term of the series $\frac{1}{4} - \frac{1}{2} + 1 \ldots$

Similar Questions

If $a, b, c$ are positive integers,then $(a + b)(b + c)(c + a)$ is

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