STEP - BY - STEP EXPLANATION
What to find?
The next term of the sequence.
The rule for the nth term.
Given:
2, 3, 4, 5
[tex]a_n=a_1+(n-1)d[/tex]
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
[tex]\begin{gathered} a_5=2+(5-1)1 \\ \\ =2+4 \\ \\ =6 \end{gathered}[/tex]
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.
[tex]a_n=2+(n-1)1[/tex][tex]a_n=2+n-1[/tex][tex]\begin{gathered} a_n=2-1+n \\ \\ =1+n \end{gathered}[/tex]
Hence, the rule for the nth-term is n+1
ANSWER
Next term = 6
Rule for nth term is n+1
