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 + 6n − 8

Answer 1

To find the first five terms of the sequence defined by the formula \( a_n = 10n^2 + 6n - 8 \), we will substitute \( n \) with 1, 2, 3, 4, and 5.

1. For \( n = 1 \):
\[
a_1 = 10(1)^2 + 6(1) - 8 = 10 \cdot 1 + 6 \cdot 1 - 8 = 10 + 6 - 8 = 8
\]

2. For \( n = 2 \):
\[
a_2 = 10(2)^2 + 6(2) - 8 = 10 \cdot 4 + 6 \cdot 2 - 8 = 40 + 12 - 8 = 44
\]

3. For \( n = 3 \):
\[
a_3 = 10(3)^2 + 6(3) - 8 = 10 \cdot 9 + 6 \cdot 3 - 8 = 90 + 18 - 8 = 100
\]

4. For \( n = 4 \):
\[
a_4 = 10(4)^2 + 6(4) - 8 = 10 \cdot 16 + 6 \cdot 4 - 8 = 160 + 24 - 8 = 176
\]

5. For \( n = 5 \):
\[
a_5 = 10(5)^2 + 6(5) - 8 = 10 \cdot 25 + 6 \cdot 5 - 8 = 250 + 30 - 8 = 272
\]

Thus, the first five terms of the sequence are:

- \( a_1 = 8 \)
- \( a_2 = 44 \)
- \( a_3 = 100 \)
- \( a_4 = 176 \)
- \( a_5 = 272 \)

In summary, the first five terms are: **8, 44, 100, 176, 272**.