Question

If thr ratio of the sum of first n terms of two A.P's is (7n + 1) : (4n + 27), find the ratio of the mth terms..
Plzz explain with steps...

Answer 1

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Answer 2

HELLO DEAR




GIVEN RATIO OF SUM OF N TERMS OF TWO AP’s

= (7n+1):(4n+27)--------------(1)

Let’s consider the ratio these two AP’s mth

terms as am : a’m →(2)the nth term of AP

formula, an = a + (n – 1)d


equation (2) ,

am : a’m = a + (m – 1)d : a’ + (m – 1)d’

On multiplying by 2,

we get


am : a’m

= [2a + 2(m – 1)d] : [2a’ + 2(m – 1)d’]


= [2a + {(2m – 1) – 1}d] : [2a’ + {(2m – 1) – 1}d’]


= S2m – 1 : S’2m – 1


= [7(2m – 1) + 1] : [4(2m – 1) +27] [using---(1)]


= [14m – 7 +1] : [8m – 4 + 27]


= [14m – 6] : [8m + 23]


Thus the ratio of mth terms of two AP’s is

[14m – 6] : [8m + 23].


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