Let b_0 = 0 and b_n = b_{n-1} + n. What is b_5?

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Multiple Choice

Let b_0 = 0 and b_n = b_{n-1} + n. What is b_5?

Each step adds the current index to the previous value, so the terms accumulate the sum of the integers from 1 up to n. Starting from zero: b1 = 0 + 1 = 1 b2 = 1 + 2 = 3 b3 = 3 + 3 = 6 b4 = 6 + 4 = 10 b5 = 10 + 5 = 15 So b5 equals 15. This aligns with the formula for the sum of the first n integers, b_n = n(n+1)/2, and for n = 5 that gives 5×6/2 = 15.

Each step adds the current index to the previous value, so the terms accumulate the sum of the integers from 1 up to n. Starting from zero:

b1 = 0 + 1 = 1

b2 = 1 + 2 = 3

b3 = 3 + 3 = 6

b4 = 6 + 4 = 10

b5 = 10 + 5 = 15

So b5 equals 15. This aligns with the formula for the sum of the first n integers, b_n = n(n+1)/2, and for n = 5 that gives 5×6/2 = 15.

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