Question

The 12th term of the arithmetic sequence is 10.5. The 18th term of this sequence is 13.5. Find the common difference and the first term.

Answer 1

Common difference = 0.5

First term = 6.

Explanation:

the 12th term a12 = a1 + d(12-1) where a1 = first term and d = the common difference.

So a1 + 11d = 10.5 ....(A) Similarly:

a1 + 17d = 13.5....(B)

Subtracting equations:

(B) - (A) :-

6d = 13.5 - 10.5 = 3

d = 3/6 = 0.5

From equation (A):

a1 + 11(0.5) = 10.5

a1 = 10.5 -5.5 = 5.