Question

the first of 6 terms of an ap is 42 the ratio of 10th term to the 30 th term of an ap is one by three calculate the first term and the 18th term

Answer 1

As usual, Let the first term be a and the common difference be d

thus, A to Q,

S6 = 42

=> 6/2 (2a + 5d) = 42

=> 3 (2a + 5d) = 42

=> 2a + 5d = 14 ----- (i)

Again, T10/T30 = 1 : 3

=> (a + 9d)/(a + 29d) = 1/3

=>a + 29d = 3a + 27d

=> 2a - 2d = 0

=> a - d = 0 --------- (ii)

On solving (i) and (ii) we get,

a = 2 and d = 2

Thus, first term = 2 and Thirteenth term = 2 + 12(2) = 2 + 24 = 26 Ans....!!!!