Question

The third term in an arithmetic sequence is 10 and the fifth term is 26.If the first term is a1,which is an equation for the nth of this sequence? please help idk how to do this.

a. an=8n 10
b. an=8n-14
c. an=16n 10
d. 16n-38

Answer 1

`a_3=10 \\ a_5=26`

The fifth term is the third term plus twice the common difference.

`a_5=a_3+2d \\ 26=10+2d \\ 26-10=2d \\ 16=2d \\ (16)/(2)=d \\ d=8`
The common difference is 8.

The third term is the first term plus twice the common difference.

`a_3=a_1+2d \\ 10=a_1+2 * 8 \\ 10=a_1+16 \\ 10-16=a_1 \\ a_1=-6`
The first term is -6.

The formula for the nth term of an arithmetic sequence:

`a_n=a_1+d(n-1) \\ \Downarrow \\ a_n=-6+8(n-1) \\ a_n=-6+8n-8 \\ \boxed{a_n=8n-14} \\ \boxed{\hbox{answer B}}`