Question

1. The 8th term of an arithmetic sequence is 12 and its
12th term is 8. What is the algebraic expression for this
sequence?
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Answer 1

Answer:

20 - n.

Step-by-step explanation:

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.    { 1 }

12th term = 8 = a + (12-1)d = a + 11d.  { 2 }

Solving equations { 1 } & { 2 } simultaneously,

we get d = -1.

Putting d in either equation,

we get a = 19.

∴ , algebraic expression for this sequence is nth term

= 19 - (n-1)

= 19 - n + 1

= 20 - n.