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+1 vote
2.7k views
in Mathematics by (284 points)

If the sum of 'n'​​​​​​ terms of two different AP are in ratio (2n+4) : (5n+5),then find the respective ratio of their 12th terms.

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2 Answers

0 votes
by (648 points)
{n/2(2a1+(n-1)d1}/{n/2(2a2+ (n-1)d2} =(2n+4)/(5n+5)

Where a1,a2 are first terms of two APs and d1 and d2 are common difference.

We have

{(2a1+(n-1)d1}/{2a2+(n-1)d2}=(2n+4)/(5n+5)

Putting n=25 we have

(A1)12/(A2)12 = 54/130=27/65
by (284 points)
Wrong answer
by (194 points)
–1
Actually, the solution is perfect. But, he had found ratio of 13th terms by putting n = 25 (instead n = 23 will give the correct answer). Anyways +1
+2 votes
by (194 points)

Given, (2n + 4) / (5n + 5) = { 2a1 + (n-1) d1 } / { 2a2 + (n-1) d2 }

Putting n = 1, we get a2 = 5/3 a1 .....(1)

Putting n = 2 and n = 3, we get,

d1 = 2/5 d2 .....(2)

3/5 d2 = a1 ......(3)


So, we have the relations b/w a1, a2, d1 and d2. Hence, the ratio comes as 5/12

by (284 points)
CORRECT ANSWER

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