if 6th term and 8th term of arithmatic sequence is -14 and -20 .find the 15th term

Question

the sixth term and eight term of arithmatic sequence is -14 and -20.find the fifteenth term

Answer 1

In arithmatic sequence n th term is a+(n-1)d

a is first term and d is common difference.

Given 6th term is a+5d = -14

8th term is a+7d = -20

Subtract 8th term from 6th term.

a+5d = -14

a+7d = -20

(-) (-)    (+)

__________

-2d = 6

Divide by negitive 2 to each side.

-2d/-2 = 6/-2

d = -3

Substitute the d value in 6th term.

a+5*-3 = -14

a-15 = -14

Add 15 to each side.

a-15+15 = -14+15

a = 1

So the first term is 1 and common difference is -3.

15th term = a+14d

= 1+14*-3

= 1-42

= -41

15th term is -41.