The sum of first n-terms of 2 AP's are in the ratio (n + 7): (3n+11) then the ratio of
their 9th term is
(A) 31:12
(B) 40:49
(C) 49:40
(D) 12:31
Answers
Answer:
Step-by-step explanation:
Given ratio of sum of n terms of two AP’s = (n+7):(3n+11)
We can consider the 9th term as the m th term.
Let’s consider the ratio these two AP’s m th 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
= [(2m – 1) + 7] : [3(2m – 1) +11] [from (1)]
= [2m+6] : [6m+8]
Thus the ratio of mth terms of two AP’s is [2m+6] : [6m+8].
now substitute the value of m as 9
so the answer becomes
24:62
which can be simplified as
12:31
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