Question

How to use two terms to find a1,d, and an For the arithmetic sequence?

Answer 1

Answer:

  d = (a[n2] -a[n1])/(n2 -n1)

  a1 = a[n1] -d(n1 -1)

Step-by-step explanation:

The generic term is ...

  an = a1 +d(n -1)

Fill in the values associated with the two terms and solve the simultaneous equations.

For terms n1 and n2, their difference will be ...

  a[n2] -a[n1] = (a1 +d(n2 -1)) -(a1 +d(n1 -1)) = d(n2 -n1)

Dividing by the coefficient of d tells you ...

  d = (a[n2] -a[n1])/(n2 -n1)

Once you have the value of d, you can find the first term.

  a[n1] = a1 +d(n1 -1)

  a1 = a[n1] -d(n1 -1)

_____

Example:

  3rd term = 12

  7th term = 20

  d = (20 -12)/(7 -3) = 8/4 = 2

 a1 = a3 -d(3 -1) = 12 -2(2) = 8

The n-th term is ...

  an = a1 +d(n -1)

  an = 8 +2(n -1)