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Venkatesh

Nov 13, 2013

# The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).

The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.

Syeda

Member since Jan 25, 2017

Answer. 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].

Agam Gupta

Member since Sep 21, 2013

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].

Dinesh Singha

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].

Priyanshu

Member since Nov 29, 2016

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].

Kishore Kumar

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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