Question

The ratio of the 11th term to the 18th term of an ap is 2 is to 3 find the ratio of the 5th term to the 21st term and also the ratio of the sum of the first 5 terms to the sum of the first 21 terms

Answer 1

Given t11 : t18 = 2 : 3  ⇒ 3a + 30d = 2a + 34d ∴ a = 4d → (1) Consider, t5 : t25 = (a + 4d) : (a + 24d)                                = (4d + 4d) : (4d + 24d)                                = 8d : 28d =  2 : 7 Hence ratio of 5th term to the 21st term is 2:7Consider S5 : S21 Therefore S5 : S21 = 5:49