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Chapter 12: Q. 35 (page 816)

Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term.
14th term is -1; 18th term is-9

Short Answer

Expert verified

The solution isa1=25andd=-2;a1=25,an=an-1-2;an=27-2n.

Step by step solution

01

Step 1. Given information 

14th term is -1; 18th term is-9

02

Step 2. Calculation 

We know that an=a1+n-1d. As a result,

a14=a1+13d=-1 鈫�1

a18=a1+17d=-9 鈫�2

Subtract the second equation from the first, we get -

-4d=8

d=-2

Substitute d=-2in a1=-1-13d=-1-13-2=25.

Therefore the first term is a1=25and the common difference isd=-2.

03

Step 3. Calculation 

Using formula -

a1=a,an=an-1+d

a recursive formula for the sequence is -

a1=25,an=an-1-2

04

Step 4. Calculation 

Using formula -

an=a1+n-1d

a formula for the nth term of the sequence is -

an=25+n-1-2

=25-2n+2

=27-2n

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