Q. 93.6( 119 Votes )

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.

Answer :

Let a1, a2, and d1, d2 be the first terms and the common difference of the first and second arithmetic progression respectively.

We know that Sum of n terms of an A.P is given by,

where, n = number of terms, a = first term and d = common difference of A.P.

So now we have,

Now as we need to find the ratio of first 17 terms, we want the numerator and denominator of the form (a + 17 d)
2 a1 + (n - 1) d1 = a + 17 d 
So we need to multiply R.H.S by 2 and we get,
2 a1 + (n - 1) d = 2 a + 34 d
Equating the terms we get,
n - 1 = 34, n = 35.

Putting n = 35 in the above equation

Thus, the ratio of 18th term of both the A.P.s is 179: 321

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