Find the Second Term t_n=2n^2-n

$t_{n} = 2 n^{2} - n$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$t_{2} = 2 {(2)}^{2} - (2)$

Step 2

Simplify each term.

Multiply $2$ by ${(2)}^{2}$ by adding the exponents.

Multiply $2$ by ${(2)}^{2}$ .

Raise $2$ to the power of $1$ .

$t_{2} = 2 {(2)}^{2} - (2)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$t_{2} = 2^{1 + 2} - (2)$

Add $1$ and $2$ .

$t_{2} = 2^{3} - (2)$

Raise $2$ to the power of $3$ .

$t_{2} = 8 - (2)$

Multiply $- 1$ by $2$ .

$t_{2} = 8 - 2$

Step 3

Subtract $2$ from $8$ .

$t_{2} = 6$