Question

The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is ______.

पर्याय

• 4

• 5

• 3

• 2

Answer 1

The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of the AP is 3.

Explanation:

 Let a be the first term and d the common difference.

t₅ = a + 4d

= 20

t₇ + t₁₁ = (a + 6d) + (a + 10d)

= 2a + 16d

= 64

Substitute a = 20 – 4d into 2a + 16d = 64:

2(20 − 4d) + 16d = 64

⇒ 40 + 8d = 64

⇒ d = 3