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 a _{1}, a_{2}, and d_{1}, d_{2} be the first terms and the common difference of the first and second arithmetic progression respectively.**

**Given: **

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.

⇒ **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 a _{1} + (n - 1) d_{1} = a + 17 d So we need to multiply R.H.S by 2 and we get,2 a_{1} + (n - 1) d = 2 a + 34 dEquating the terms we get,n - 1 = 34, n = 35.**

Putting n = 35 in the above equation

⇒

⇒

∴

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

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