strong{font-weight:bold !important}e Number Sequence: 3, 9, 21, 45, ?To determine the next number in the sequence, we observe the pattern in the differences between consecutive terms:9 - 3 = 621 - 9 = 1245 - 21 = 24These differences are: 6, 12, and 24, each doubling the previous difference. This suggests that the sequence follows a pattern where each term is obtained by adding twice the previous difference to the current term.To find the next term:Next difference: 24 × 2 = 48Next term: 45 + 48 = 93Therefore, the next number in the sequence is 93.Solution Explanation:The sequence follows a pattern where each term is obtained by adding twice the previous difference to the current term. This can be represented by the recursive formula:an = an-1 + 2 × (an-1 - an-2)Applying this formula:a1 = 3a2 = 9a3 = 21a4 = 45a5 = 45 + 2 × (45 - 21) = 45 + 2 × 24 = 45 + 48 = 93Thus, the next number is 93.

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Detailed Solution

e Number Sequence: 3, 9, 21, 45, ?

To determine the next number in the sequence, we observe the pattern in the differences between consecutive terms:

9 - 3 = 6
21 - 9 = 12
45 - 21 = 24

These differences are: 6, 12, and 24, each doubling the previous difference. This suggests that the sequence follows a pattern where each term is obtained by adding twice the previous difference to the current term.

To find the next term:

Next difference: 24 × 2 = 48
Next term: 45 + 48 = 93

Therefore, the next number in the sequence is 93.

Solution Explanation:

The sequence follows a pattern where each term is obtained by adding twice the previous difference to the current term. This can be represented by the recursive formula:

a_n = a_n-1 + 2 × (a_n-1 - a_n-2)

Applying this formula: