Question

the sum of n term of two AP are in the ratio (7n + 1): (4n + 27) find the ratio of the 11th term
answer is 4:3

Answer 1

heya!!! mate
ur answer ..here

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)


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]....

hope helps u dear. ..