The next term of the A.P. 7 , 28 , 63 ,… - Infinity Learn by Sri Chaitanya

Given an AP

\sqrt{7}, \sqrt{28}, \sqrt{63}, . . . .

Examine the given conditions.

⇒ 7, 28, 63, ..... ⇒ 7, 4 × 7, 9 × 7, ..... ⇒ 7, 27, 37, ....

Therefore,

⇒ a = 7 ⇒ d = 27 − 7 ⇒ d = 7

Hence, the next term i.e., 4th term will be,

\Rightarrow a_{n} = a + (n - 1) d

\Rightarrow a_{4} = \sqrt{7} + (4 - 1) \sqrt{7}

\Rightarrow a_{4} = \sqrt{7} + 3 \sqrt{7}

⇒ 47 ⇒ 16 × 7 ⇒ 112

Therefore, next term of an AP

\sqrt{7}, \sqrt{28}, \sqrt{63}, . . . .

\sqrt{112}

.
Hence, the correct option is 4.

The next term of the A.P. $7, 28, 63, …$