Question

If the 3rd term of an arithmetic sequence is 2 and the 17th term is -40, find the 7th term

Answer 1

-10

Explanation:

t3 = a1 + (n - 1)*d

t3 = a1 + (3 -1)*d

2 = a1 + 2d

t17 = a1 + (n - 1)*d

-40 = a1 + 16d Put the first condition underneath and subtract

2 = a1 + 2d

-42 = 14 d

d = - 3

2 = a1 + 2*(-3)

2 = a1 - 6 Add 6 to both sides

2 + 6 = a1

a1 = 8

Now you want the 7th term

t7 = a1 + (n - 1)*d

t7 = 8 + (7 - 1)*d

t7 = 8 + 6*(-3)

t7 = 8 - 18

t7 = - 10