Question

I need help with my homework PLEASE CHECK WHEN DONE ANSWERING

Answer 1

The sequence is given below as

`8,11,14,17,20`

Step 1:

The nth term of an arithmentic progression is given below as

`\begin{gathered} a_n=a+(n-1)d \\ where, \\ a=first\text{ term} \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}`

To figure out the common difference, we will use the formula below

`\begin{gathered} d=a_2-a_1=a_3-a_2 \\ d=11-8=14-11=17-14=20-17=3 \\ d=3 \end{gathered}`

Step 2:

The first term of the sequence is given below as

`a=8`

Step 3:

Substitute the value of a and d in the formula below

`\begin{gathered} a_(n)=a+(n-1)d \\ a_n=8+(n-1)3 \\ a_n=8+3n-3 \\ a_n=5+3n \end{gathered}`

Hence,

The final answer is

`a_n=5+3n,where\text{ n=1,2,3,4,...}`

OPTION A is the right answer