Test Index

Sequence and Series

Question : 58 of 86

Marks: +1, -0

If the

n^{\;\text{th }\;}

(3n+1):(n+4)

the ratio of the fourth term is

Solution:

Concept:

The ratio of the

n^{\text{th}}

terms of two APs is given as

\frac{3n+1}{n+4}

. The ratio of their fourth terms is found by substituting

n=4

if the ratio holds for all

n

, but we verify by solving for the AP parameters.

Explanation:

Let the

n^{\text{th}}

terms be

T_{1,n} = a_1 + (n-1)d_1

and

T_{2,n} = a_2 + (n-1)d_2

Given

\frac{T_{1,n}}{T_{2,n}} = \frac{3n+1}{n+4}

Cross-multiply:

(a_1-d_1 + d_1 n)(n+4) = (a_2-d_2 + d_2 n)(3n+1)

Equate coefficients of

n^2

n

, and constant

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