question - If the ratio of the sum of the first n terms of two APs is ( 7n+1 ) : ( 4n+27 ) then find the ratio of their 9th terms..
PLEASE ANY ONE SOLVE THIS QUESTION WITH EXPLANATION...
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Answers
Answer:
64:63
Step-by-step explanation:
(7n+1):(4n+27)
n=9
7(9)+1 :4(9)+27
63+1 :36+27
64:63
Answer:
Given ratio of sum of n terms of two AP's = (7n+1):(4n+27) 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 : a² + (m – 1)d' am : a'm = [2a + 2(m − 1)d] : [2a' + 2(m −
On multiplying by 2, we get
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].
now substitute the value of m as 9
so the answer becomes
120/95
I have given you right answer now