Question

PLEASE HELP QUICK !!!

Answer 1

The explicit equation is
`\mathbf{a_n=5n+3}`

Option A is correct option.

Explanation:

Third term of sequence is 18

Sixth term of sequence is 33

We need to find the explicit equation for the sequence.

The explicit sequence is
`a_n=a_1+(n-1)d`

We need to find a_1 the first term and common difference d

We have a₃=18

We can write it as:
`a_3=a_1+(3-1)d\\`

`18=a_1+2d`

a₆=33

We can write it as:
`a_6=a_1+(6-1)d\\33=a_1+5d`

Now, solving these equation s we can find value of d

`18=a_1+2d`

`33=a_1+5d`

Subtract both equations

`18=a_1+2d`

`33=a_1+5d`

`--------\\-15=-3d\\d=(-15)/(-3)\\d=5`

So, we get common difference d = 5

Now finding a_1

Put value of d in equation
`18=a_1+2d`

`18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8`

So, we get a₁ = 12

Now, the explicit equation is:

`a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3`

So, the explicit equation is
`\mathbf{a_n=5n+3}`

Option A is correct option.