Posted by **Anonymous** on Tuesday, December 17, 2013 at 10:34am.

the third term of an arithmetic sequence is 14 and the ninth term is -1. Find the first four terms of the sequence

- algebra -
**bobpursley**, Tuesday, December 17, 2013 at 10:38am
ninth -1, third 14

it goes now by 15 in six steps; step 15/6 or 2.5

third through tenth terms

14, 11.5, 9, 6.5, 4, 1.5, -1, -3.5,...

check that

- algebra -
**Chelle**, Friday, January 3, 2014 at 9:00pm
third term is 14 and ninth term is -1

14 - 2.5 = 11.5 > 4th term

11.5 - 2.5 = 9 > 5th term

9 - 2.5 = 6.5 > 6th term

6.5 - 2.5 = 4 > 7th term

4 - 2.5 = 1.5 > 8th term

1.5 - 2.5 = -1 > 9th term

The terms are decreasing by 2.5 > (-2.5)

To go from one term to the next, subtract 2.5.

The common difference is -2.5

d = -2.5

Arithmetic Sequence Formula:

Tn = Tn + d(n-1)

a = 1st term

n = nth term

d = common difference

We don't know the first term yet!

Tn = T1 + d(n-1)

Substitute 3 for n, and -2.5 for d

T3 = T1 + -2.5(3-1)

Now substitute 14 for T3

14 = T1 + -2.5(2)

14 = T1 -5

14 + 5 = T1 -5 +5

19 = T1

T1 = 19

T2 = 16.5

T3 = 14

T4 = 11.5

Now to find a term:

Tn = T1 + d(n-1)

T2 = 19 + -2.5(2-1) T3 = 19 + -2.5(3-1)

T2 = 19 + -2.5(1) T3 = 19 + -2.5(2)

T2 = 19 + -2.5 T3 = 19 + -5

T2 = 16.5 T3 = 14

__________________________

You can also use this formula:

Tn = dn + 21.5

T1 = -2.5(1) + 21.5

T1 = 19

T4 = -2.5(4) + 21.5

T4 = 11.5

T9 = -2.5(9) + 21.5

T9 = -1

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