If the ratio of sums to n terms of two AP's is (5n+3) : (3n+4), then what is the ratio of their 17th terms? [3 MARKS]

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Solution

Concept: 1 Mark
Application: 2 Marks

According to the given condition.

$\frac{\frac{n}{2} [2 a + (n - 1) d]}{\frac{n}{2} [2 A + (n - 1) D]} = \frac{5 n + 3}{3 n + 4}$

$\Rightarrow \frac{a + \frac{n - 1}{2} d}{A + \frac{n - 1}{2} D} = \frac{5 n + 3}{3 n + 4}$

For the ratio of the 17th terms,
$\frac{n - 1}{2} = 16$

$n = 33$

$\Rightarrow \frac{a + 16 d}{A + 16 D} = \frac{5 (33) + 3}{3 (33) + 4}$

$= \frac{168}{103}$

$= 168 : 103$

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