Question

Determine the A.P. whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Answer 1

In an A.P.,
T₅ = 19
T₁₃ – T₈ = 20
Let a be the first term and d be the common difference
∴ T₅ = a + 4d = 19                           ...(i)
T₁₃ – T₈ = (a + 12d) – (a + 7d)
⇒ 20 = a + 12d – a – 7d
⇒ 20 = 5d
⇒ d = `(20)/(5)` = 4
Substitute the value of d in eq. (i), we get
∴ a + 4 x 4 = 19
⇒ a + 16 = 19
⇒ a = 19 – 16 = 3
∴ A.P. is 3, 7, 11, 15,...