Question

The 8th term of an arithmetic sequence is 12 and it's 12th term is 8.What is the algebraic expression for this sequence?

Answer 1

Answer:

Let the first term of the A.P. be a. Let its common difference be d. As we know, nth term of an A.P. = a + (n-1)d.

Given:

8th term = 12 = a + (8-1)d = a + 7d. This is equation 1.

12th term = 8 = a + (12-1)d = a + 11d. This is equation 2.

Solving equations 1 and 2 simultaneously, we get d = -1. Putting d in either equation, we get a = 19.

Therefore, algebraic expression for this sequence is nth term = 19 - (n-1) = 19 - n + 1 = 20 - n.

Hope this helps.

Answer 2

Answer:

Step-by-step explanation:

:common difference= -1

=xn=an+b

Ie 12=-8+b

:b=12+8=20

Algebraic expression of the given sequence.

Xn=-1×n+20

Ie Xn =20-n