Question

If 'n' AMs are inserted between 1 and 51, and the ratio of 4th term to the 7th term is 3:5, find the value of n

Answer 1

go through the solution step by step

Answer 2

Answer: 24

Step-by-step explanation:

first term of this AP series is 1 , so a =1

now nth term(Tn) = a+(n-1)d (d is common ration of this series)

4th term of AMs means 5th term of AP ...so T5 = a+4d = 1+ 4d

7th term of AMs means 8th term of AP ...so T8 = a+7d = 1+7d

ratio is given = 3/5

1+4d/1+7d = 3/5

5+20d = 3+21d

d = 2

now ,let there are n terms in this Ap then

There are n+2 terms in the AP because we’re also including 1 and 51

Therefore

1 + (n+1)d = 51

so n = 24

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