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.
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.
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
Rate this question :
Find the second term and nth term of an A.P. whose 6th term is 12 and 8th term is 22.RD Sharma - Mathematics
There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.RD Sharma - Mathematics
If x, y, z are in A.P. and A1is the A.M. of x and y, and A2 is the A.M. of y and z, then prove that the A.M. of A1 and A2 is y.RD Sharma - Mathematics
Insert 7 A.M.s between 2 and 17.RD Sharma - Mathematics
The 10th and 18th term of an A.P. are 41 and 73 respectively, find 26th term.RD Sharma - Mathematics
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that the 25th term of the A.P. is Zero.RD Sharma - Mathematics
Insert five numbers between 8 and 26 such that the resulting sequence is an A.PRD Sharma - Mathematics
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.RD Sharma - Mathematics
In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112RD Sharma - Mathematics
Insert 4 A.M.s between 4 and 19.RD Sharma - Mathematics