Question

Find the Next Number - 1, 4, 9, 16, 25, 36, 49, ?
Find the next number of the following series? 1, 4, 9, 16, 25, 36, 49, ? A) 54 B) 56 C) 64 D) 81

Answer 1

The answer is 64(c).

Answer 2

Answer:

The next number in the series is 64.

Step-by-step explanation:

• The given series is 1 , 4 , 9 , 16 , 25 , 36 , 49...
• On carefully examining the series one can see that series successive terms are square of natural numbers:

${1}^{2} = 1 \times 1 = 1 \\ {2}^{2} = 2 \times 2 = 4 \\ {3}^{2} = 3 \times 3 = 9 \\ {4}^{2} = 4 \times 4 = 16 \\ {5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49 \\ and \: so \: on$

• Next number of the series must be square of 8, i.e. 8 x 8 = 64.
• Hence, next number in the series is 64.