Question

The 4th term of an AP is 14 and its 12th term is 70. What is its first term?
(a) 7
(b) 10
(c) −7
(d) −10

Answer 1

( c) -7
T₄ = a + 3d = 14 ...(i)
T₁₂ = a + 11d = 70 ...(ii)
On subtracting (i) from (ii), we get:
⇒ 8d = 56
⇒ d = 7

On putting the value of d in (i), we get:
⇒ a + 3 $\times$ 7 = 14
⇒ a = -7
Hence, the first term is -7.