Question

plese tell me Question no1

Answer 1

Given ratio of sum of n terms of two AP’s = (7n+1) : (4n + 27)
Let’s consider the ratio of these two AP’s mthterms as am : Am -------------(2)
nth term of AP formula, an = a + (n – 1)d
Hence equation (2) becomes,
am : Am = a + (m – 1)d : a’ + (m – 1)d’
On multiplying by 2, we get
am : Am = [2a + 2(m – 1)d] : [2a’ + 2(m – 1)d’]
= [2a + {(2m – 1) – 1}d] : [2a’ + {(2m – 1) – 1}d’]
= S(2m – 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].