If the ratio of the sum of first n terms of two AP's is (7n+1):(4n+27), find the ratio of their mth terms.
babu11110:
hi
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Refer the attached picture.
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How -1 ??
2( m - 1 ) = 2m - 2 , it can also be written as ( 2m - 1 - 1) = {( 2m - 1) - 1}
But he has written it in bracket!!??
It is in multiplication no!!
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Bracket is used for ( 2m - 1 ) and - sign is after the bracket, so it will mean subtraction, not multiplication. Like = { ( 2m - 1 ) - 1}
Ohk!!!
If we write it as {( 2m - 1) ( - 1 )}, then it will be in multiplication.
Oh!!! yup I got it thanks a lot!!
Welcome :-)
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Step-by-step explanation:
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Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27) Let’s consider the ratio these two AP’s mth terms as am : a’m →(2) Recall the nth term of AP formula, an = a + (n – 1)d Hence equation (2) becomes, 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] [from (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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