If the 4th term of an arithmetic progression is 14 and the

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If the 4th term of an arithmetic progression is 14 and the 12th term is 70, then the first term is :

1. – 10
2. – 7
3. + 7
4. + 10

Correct Option: B

Here , a₄ = 14 , a₁₂ = 70
Using the given formula ,
a₄ = a₁ + (4 – 1) × d
14 = a₁ + 3d
⇒ a₁ = 14 – 3d ....(i)
70 = a₁ + 11d ....(ii)
After putting the value of a₁ in equation (i)
⇒ 14 – 3d + 11d = 70
⇒ 8d = 70 – 14
⇒ d = 7
∴ a₁ = 14 – 21 = – 7