Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1. an = 7n2 − 5n − 6 , ,

Answer 1

To find the first three terms of the sequence defined by the formula \( a_n = 7n^2 - 5n - 6 \), we will substitute values of \( n \) starting from 1.

1. For \( n = 1 \): \[ a_1 = 7(1)^2 - 5(1) - 6 = 7(1) - 5 - 6 = 7 - 5 - 6 = -4 \]

2. For \( n = 2 \): \[ a_2 = 7(2)^2 - 5(2) - 6 = 7(4) - 10 - 6 = 28 - 10 - 6 = 12 \]

3. For \( n = 3 \): \[ a_3 = 7(3)^2 - 5(3) - 6 = 7(9) - 15 - 6 = 63 - 15 - 6 = 42 \]

Putting it all together, the first three terms of the sequence are: \[ a_1 = -4, \quad a_2 = 12, \quad a_3 = 42 \]

Therefore, the first three terms are \(-4\), \(12\), and \(42\).