Question

It says write the next term of the sequence. Then write the rule for the n-th term?

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

The next term of the sequence.

The rule for the nth term.

Given:

2, 3, 4, 5

`a_n=a_1+(n-1)d`

where a1 is the first term, n is the number of term and d is the common difference.

Step 1

Identify the first term and determine the common difference.

a1 = 2

d= 4 - 3 = 1

Step 2

Substitute the values into the formula to determine the next term.

Since the next term is the fifth term, then n=5

`\begin{gathered} a_5=2+(5-1)1 \\ \\ =2+4 \\ \\ =6 \end{gathered}`

Hence, the next term is 6

Step 3

Determine the rule of the nth term.

Substitute the value of a1 and d into the formula.

`a_n=2+(n-1)1`
`a_n=2+n-1`
`\begin{gathered} a_n=2-1+n \\ \\ =1+n \end{gathered}`

Hence, the rule for the nth-term is n+1

ANSWER

Next term = 6

Rule for nth term is n+1