Question

Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = 10n2 − 7n + 10

Answer 1

To find the first five terms of the sequence defined by the formula \( a_n = 10n^2 - 7n + 10 \), we will calculate the value of \( a_n \) for \( n = 1, 2, 3, 4, \) and \( 5 \).

1. For \( n = 1 \):
\[
a_1 = 10(1^2) - 7(1) + 10 = 10(1) - 7 + 10 = 10 - 7 + 10 = 13
\]

2. For \( n = 2 \):
\[
a_2 = 10(2^2) - 7(2) + 10 = 10(4) - 14 + 10 = 40 - 14 + 10 = 36
\]

3. For \( n = 3 \):
\[
a_3 = 10(3^2) - 7(3) + 10 = 10(9) - 21 + 10 = 90 - 21 + 10 = 79
\]

4. For \( n = 4 \):
\[
a_4 = 10(4^2) - 7(4) + 10 = 10(16) - 28 + 10 = 160 - 28 + 10 = 142
\]

5. For \( n = 5 \):
\[
a_5 = 10(5^2) - 7(5) + 10 = 10(25) - 35 + 10 = 250 - 35 + 10 = 225
\]

Now we can summarize the first five terms of the sequence:

- \( a_1 = 13 \)
- \( a_2 = 36 \)
- \( a_3 = 79 \)
- \( a_4 = 142 \)
- \( a_5 = 225 \)

Thus, the first five terms of the sequence are: **13, 36, 79, 142, 225**.