Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions3 Marks
Question
The sums of first n terms of two A.P.'s are in the ratio $(7n + 2) : (n + 4)$. Find the ratio of their $5th$ terms.
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Answer
Let sum of n term 1 A.P series are other $s_n$ The, $\text{s}_\text{n}7\text{n}+2\ .....(1)$
$\text{s}_\text{n}=\text{n}+4\ .....(2)$ the ratio of sum of n terms of A.P is given, then the ratio of there $n^{th}$ term is obtained by (2n - 1). $\frac{\text{a}_\text{n}}{\text{a}_\text{n}}=\frac{7(2\text{n}-1)+2}{(2\text{n}-1)+4}$ Putting n = 5 to get the ratio of 5th term,
we get $\frac{\text{a}_5}{\text{a}_5}=\frac{7(2\times5-1)+1}{(2\times5-1)+4}=\frac{65}{13}=\frac{5}{1}$ The ratio is 5 : 1
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