list the first five terms of the sequences with on term \( 3 n^{2}+10 \)

To find the first five terms of the sequence defined by the formula \( 3n^2 + 10 \), we will substitute \( n = 1, 2, 3, 4, \) and \( 5 \) into the formula. 1. For \( n = 1 \): \[ 3(1^2) + 10 = 3(1) + 10 = 3 + 10 = 13 \] 2. For \( n = 2 \): \[ 3(2^2) + 10 = 3(4) + 10 = 12 + 10 = 22 \] 3. For \( n = 3 \): \[ 3(3^2) + 10 = 3(9) + 10 = 27 + 10 = 37 \] 4. For \( n = 4 \): \[ 3(4^2) + 10 = 3(16) + 10 = 48 + 10 = 58 \] 5. For \( n = 5 \): \[ 3(5^2) + 10 = 3(25) + 10 = 75 + 10 = 85 \] Thus, the first five terms of the sequence are: \[ 13, 22, 37, 58, 85 \]