Question

The eighth term of an arithmetic sequence is double the value of the third term. The fifth term is equal to 14. Determine the first term and the common difference of the sequence.

Answer 1

Answer: first term = 6

Common difference = 2

Explanation:

Eight term =a +(n-1)d = a +(8-1)d = a + 7d

Third term = a+(n-1)d = a + (3-1)d =a + 2d

a + 7d = 2(a + 2d)

a + 7d = 2a + 4d

7d - 4d = 2a - a

a = 3d

The fifth term is equal to 14. This is:

a + 4d = 14

Put the value of a into the equation here

3d + 4d = 14

7d = 14

d = 14/7

d = 2

Recall that a + 4d = 14

a + 4(2) = 14

a + 8 = 14

a = 14 - 8

a = 6