Question

the 43rd term of an arithmetic sequence is -671 and the 52nd term is -806. find the first term and the common difference.

Answer 1

First term = -41.

Common difference = -15.

Explanation:

nth term: an = a1 + (n - 1)d where a = first term and d = the common difference.

-671 = a1 + (43 - 1)d

-806 = a1 +(52 - 1)d

-671 = a1 + 42d

-806 = a1 + 51d

Subtracting ( to eliminate a1):

-671 - (-806) = 42d - 51d

-9d = 135

d = -15

Substitute for d in the first equation:

-671 = a1 + 42*-15

-671 = a1 - 630

a1 = -671 + 630 = -41.