thinking/inquiry/problem solving: a formula for the sum of the first n terms of an arithmethic series is Sn=n^2 + 4n. determin e the first four terms of the series.
To determine the first four terms of the arithmetic series, we need to substitute the values of n from 1 to 4 into the formula Sn = n^2 + 4n and calculate the corresponding terms.
Let's start by substituting n = 1 into the formula:
S1 = 1^2 + 4(1)
S1 = 1 + 4
S1 = 5
So, the first term of the series, when n = 1, is 5.
Now, let's substitute n = 2 into the formula:
S2 = 2^2 + 4(2)
S2 = 4 + 8
S2 = 12
The second term of the series, when n = 2, is 12.
Next, we substitute n = 3 into the formula:
S3 = 3^2 + 4(3)
S3 = 9 + 12
S3 = 21
The third term of the series, when n = 3, is 21.
Now, let's substitute n = 4 into the formula:
S4 = 4^2 + 4(4)
S4 = 16 + 16
S4 = 32
The fourth term of the series, when n = 4, is 32.
Therefore, the first four terms of the series are 5, 12, 21, and 32.