Test Index

Sequence and Series

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Question : 73 of 86

Marks: +1, -0

If

\;\frac{1+3+5+\cdots+n \; \text{ terms}}{2+4+6+\cdots+50 \; \text{ terms}} = \; \frac{2}{51},

then the value of 'n'

9
10
12
13

Solution:

Concept:

Sum of first

n

odd numbers is

n^2

; sum of first

n

even numbers is

n(n+1)

.

Explanation:

The numerator

1+3+5+\cdots

up to

n

terms equals

n^2

.

The denominator

2+4+6+\cdots

up to

50

terms equals

50 \times (50+1) = 2550

.

Given

\frac{n^2}{2550} = \frac{2}{51}

.

Cross-multiply:

n^2 \times 51 = 2 \times 2550

, so

51n^2 = 5100

.

Thus

n^2 = \frac{5100}{51} = 100

, so

n = 10

(positive).

Answer:

n = 10

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