Question

1 2 3 7 16 65 what comes after 65?​

Answer 1

Answer:

321

Step-by-step explanation:

1 = 1 (First term as it is )

↓   ↓

n   N

Logic - N + n * n

1 + 1 * 1 = 2

2 + 1 * 1 = 3

3 + 2 * 2 = 7

7 + 3 * 3 = 16

16 + 7 * 7 = 65

65 + 16 * 16 = 65 +256 = 321

Answer 2

Answer:

The next number in the series is 321.

Step-by-step explanation:

Given:

1, 2, 3, 7, 16, 65, ?.

To find:

Find the term which is next to 65 in the series.

From the given series :

We can write the second term as

                            2 = 1 +  1 x 1

The third term can be written as,

                            3 =  2+ 1 x 1

The fourth term can be  written as

                            7 = 3 + 2 x 2

The fifth term  can be written as

                           16 = 7 + 3 x 3

The sixth term  can be written as

                          65 = 16 + 4 x 4

From the above, we can observe a pattern.

Each term is written as the previous term plus the square of ( n-1)th term.

In general, the nth term in the series can be written as:

                           n = prev term  + (n-1) term

65 + 16 x 16 =  321.

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