Question

An arithmetic sequence has first term (a) and the common difference (d). The sum of the first 25 terms is 15 times the sum of the first 4 terms. Find (a) ​

Answer 1

a = 12.

Explanation:

Sum of n terms = n/2[2a + d(n-1)]

For 25 terms

S25 = 12.5(2a + 24d)

S25 = 25a + 300d

For 4 terms

S4 = 2(2a + 3d)

So:

S25 = 15*2(2a + 3d)

S25 = 60a + 90d

25a + 300d = 60a + 90d

35a = 210d

a = 6d

Take a to be 12 and d to be 2:

25th term = 12.5(2*12 + 24 * 2) = 900

4th term = 2(24 + 6) = 60

900 = 15 * 60 so a = 12.