Answer:
The explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
Step-by-step 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 [tex]a_n=a_1+(n-1)d[/tex]
We need to find a_1 the first term and common difference d
We have a₃=18
We can write it as: [tex]a_3=a_1+(3-1)d\\[/tex]
[tex]18=a_1+2d[/tex]
a₆=33
We can write it as: [tex]a_6=a_1+(6-1)d\\33=a_1+5d[/tex]
Now, solving these equation s we can find value of d
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
Subtract both equations
[tex]18=a_1+2d[/tex]
[tex]33=a_1+5d[/tex]
[tex]--------\\-15=-3d\\d=\frac{-15}{-3}\\d=5[/tex]
So, we get common difference d = 5
Now finding a_1
Put value of d in equation [tex]18=a_1+2d[/tex]
[tex]18=a_1+2(5)\\18=a_1+10\\a_1=18-10\\a_1=8[/tex]
So, we get a₁ = 12
Now, the explicit equation is:
[tex]a_n=a_1+(n-1)d\\a_n=8+(n-1)5\\a_n=8+5n-5\\a_n=5n+3[/tex]
So, the explicit equation is [tex]\mathbf{a_n=5n+3}[/tex]
Option A is correct option.
