Question

Given the recursive sequence bn, find b5, where b1 = 2, b2 = 4, and bn = -2bn-1 - 3bn-2.

Answer 1

In the recursive sequence, by following the pattern, we calculate subsequent terms to find that the fifth term, b5, is 10.

Step-by-step explanation:

To find the term b5 of the recursive sequence bn where b1 = 2, b2 = 4, and the recursive formula is bn = -2bn-1 - 3bn-2, we will use the given initial terms to calculate the subsequent terms until we reach the fifth term.

• b3 = -2b2 - 3b1 = -2(4) - 3(2) = -8 - 6 = -14
• b4 = -2b3 - 3b2 = -2(-14) - 3(4) = 28 - 12 = 16
• b5 = -2b4 - 3b3 = -2(16) - 3(-14) = -32 + 42 = 10

Therefore, the fifth term of the sequence, b5, is 10.