Question

Find the first four terms of the sequence given by the formula:

c_n = n(n+1)
​a. 12, 23, 34, 45
b. 1,2,6,24
c. 0,2,6,12
d. 2,6,12,20

Answer 1

Answer: Choice D. 2, 6, 12, 20

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Work Shown:

Plug in n = 1

c(n) = n(n+1)

c(1) = 1(1+1)

c(1) = 1(2)

c(1) = 2

The first term is 2

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Plug in n = 2

c(n) = n(n+1)

c(2) = 2(2+1)

c(2) = 2(3)

c(2) = 6

The second term is 6

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Plug in n = 3

c(n) = n(n+1)

c(3) = 3(3+1)

c(3) = 3(4)

c(3) = 12

The third term is 12

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Plug in n = 4

c(n) = n(n+1)

c(4) = 4(4+1)

c(4) = 4(5)

c(4) = 20

The fourth term is 20

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The first four terms are: 2, 6, 12, 20

Answer 2

d. 2,6,12,20

Explanation:

You only need to compute c_n for n=1 to choose the correct answer:

c1 = 1(1+1) = 2 . . . . . matches choice D