Question

the ratio of the sum of n terms of two different ap is (3n+8):(7n+15).Find the ratio of the 12 terms of the two AP

Answer 1

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].

Answer 2

★ Ello ★


here is your answer !!


the ratio of AP s


3n + 8 : 7n + 15


3 ( 2m -1 ) +8 : 7( 2m -1 ) +15


m = 12


therefore ,


3 ( 24 -1 ) +8 : 7 ( 24 -1 ) +15


=> 69 + 8 : 203 + 15


=> 77 : 218


hence , the ratio is

★ 77 :218 ★


hope it helps you dear !!



$thanks$