Question

PLEASE ANSWER RIGHT AWAY

Answer 1

The second term of the sequence is 7 ⇒ the 2nd answer

Explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

the formula to be the previous term plus the common difference.

a1 = first term;

an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence

# an+1 = the term after the nth term

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ The recursive definition is tn+1 = 2 tn + n and t1 = 3

- Lets find the 2nd term

∵ t1 = 3

∵ tn+1 = 2 tn + n

* To find the second term put n = 1

∴ t2 = 2 (3) + 1

∴ t2 = 6 + 1 = 7

∴ t2 = 7

* The second term of the sequence is 7

Answer 2

The second term is 7.

EXPLANATION

The given sequence has it's first term to be:

`t_1 = 3`

The recursive definition is :

`t_(n+1)=2t_n+n`

To find the second term , we substitute n=1,

to obtain,

`t_(1+1)=2t_1+1`

This implies that:

`t_(2)=2t_1+1`

`t_(2)=2(3)+1`

Simplify:

`t_(2)=6+1`

`t_(2) = 7`