# algebra

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

1. 👍 0
2. 👎 0
3. 👁 211
1. 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

1. 👍 0
2. 👎 0
2. 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

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

what are the similarities and differences between an arithmetic sequence and a linear equation? ok i know that arithmetic sequence is a sequence of real numbers for which each term is the previous term plus a constant (called the

2. ### Algebra

What is the ninth term of the arithmetic sequence defined by the rule A(n)=-14+(n-1)(2) A)232 B)230 C)2 D)4 Thanks

3. ### math

Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 *** The sequence is neither geometric

4. ### arithmetic

The initial term of an arithmetic sequence is 5. The eleventh term is 125. what is the common difference of the arithmetic sequence?

1. ### Arithmetic Sequence

Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term.

2. ### math

The first term of an arithmetic sequence is 2.The 12th term in the progression is 9 times bigger than the 2nd term. Find the common difference d.

3. ### math

Given that the sum of the first 20 terms of an arithmetic sequence is 1150 and the fifth term is twice the second term . find: 1.The first term and the common difference 2. find the general formula

4. ### Math

1. Find the 12th term of the arithmetic sequence 2, 6, 10, … . 2. Solve for the 101st term of the sequence whose 1st term is x-y and d=2x+y-3. 3. In the sequence 2, 6, 10, … , what term has a value of 106?

1. ### mathematics

1.1 the third term of an arithmetic sequence is 8 and the 15 term is 44 . Calculate: 1.1 the common difference and first term. 1.2 the sum of the first 50 terms. 1.2 1;4;7;10.... Is an arithmetic sequence .find: 1.2.1 the 30 term.

2. ### Math

The fourth term of an arithmetic sequence is less than the fifth term by 3. The seventh term is three times the fifth term. Find the common difference and the first term

3. ### math

The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric

4. ### algebra

The second term of an arithmetic sequence is 24 and the fifth term is 3.Find the first term and the common difference.