Sequence Next 36C733

1. **Problem Statement:** Find the next number in each of the given sequences. 2. **Sequence a:** $5, 11, 17, 23, 29, 35$ - This is an arithmetic sequence increasing by $6$ each time. - Formula: $a_{n+1} = a_n + 6$ - Next number: $35 + 6 = 41$ 3. **Sequence b:** $89, 85, 81, 77, 73, 69$ - This is an arithmetic sequence decreasing by $4$ each time. - Formula: $a_{n+1} = a_n - 4$ - Next number: $69 - 4 = 65$ 4. **Sequence c:** $4, 15, 26, 37, 48, 59$ - This is an arithmetic sequence increasing by $11$ each time. - Formula: $a_{n+1} = a_n + 11$ - Next number: $59 + 11 = 70$ 5. **Sequence d:** $1, 2, 4, 8, 16, 32, 64$ - This is a geometric sequence doubling each time. - Formula: $a_{n+1} = 2 \times a_n$ - Next number: $64 \times 2 = 128$ 6. **Sequence e:** $15625, 3125, 625, 125, 25$ - This is a geometric sequence dividing by $5$ each time. - Formula: $a_{n+1} = \frac{a_n}{5}$ - Next number: $\frac{25}{5} = 5$ 7. **Sequence f (Fibonacci Sequence):** $1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89$ - Each number is the sum of the two preceding numbers. - Formula: $a_{n} = a_{n-1} + a_{n-2}$ - Next number: $55 + 89 = 144$ **Final answers:** a) $41$ b) $65$ c) $70$ d) $128$ e) $5$ f) $144$