Question

If the nth term is , then the (n+1)st is: Please make sure you check the image :)

Answer 1

`\large \boxed{\sf C. \ (n+1)/(2) (3n+2)}`

Explanation:

`\displaystyle (n)/(2) (3n-1)`

To find the (n+1)st term, replace the n variable with n+1.

`\displaystyle (n+1)/(2) (3(n+1)-1)`

Expand brackets.

`\displaystyle (n+1)/(2) (3n+3-1)`

Subtract like terms in brackets.

`\displaystyle (n+1)/(2) (3n+2)`

Answer 2

( n+1) /2 *( 3n+2)

Explanation:

n/2 * ( 3n-1)

We want the n+1 term

Replace n with n+1

( n+1) /2 *( 3( n+1) -1)

Distribute

( n+1) /2 *( 3n+3 -1)

( n+1) /2 *( 3n+2)