*(*View/Download
.pdf file*)*

#### Finding The n^{th} Term In A Sequence:

A. Many times instead
of finding the next term in a sequence you are asked to find a specific term in
a sequence. For problems like this use the following:

1. When asked this
question, almost all the sequences will be adding a fixed number to each
successive term. (See *Finding The Next Term
part C*)

2. This problem I
always approach from a logic standpoint.

3. Ask
yourself, what should the first term be? (This is 'a'.) This is always
equal to the fixed number that is being added.

4. Now,
how can I change the number in step 3 (by adding or subtracting a number) to
equal the first term? (This is 'b'.)

5. Now, make
an expression for the n^{th }term using the above information:

an + b

Ex [1] Find
the 11^{th} term of the sequence 4, 7, 10,...

a. Notice
that 3 is being added to all numbers, so the first term should be 3, then 6,
then 9, etc.

b. You
need to add 1 to 3 to equal 4.

c. So the
expression is 3n + 1.

d. The
answer is 3(11) + 1 or 34.

Ex [2] Find
the 8^{th} term of the sequence -2, 0, 2,...

a. In
this case 'a' is 2. So normally we would count: 2,4,6,etc. So the
first term should be 2.

b. If we
subtract 4 from 2 we get -2.

c. So the
expression is 2n - 4.

d. The
answer is 2(8) - 4 or 12.

Ex [3] Find
the 40^{th} term in the sequence 1, 7, 13,...

a. In
this case 'a' is 6. So the first term should be 6.

b. If we
subtract 5 from 6 we get 1.

c. So the
expression is 6n - 5.

d. The
answer is 6(40) - 5 or 235.

B.
Sometimes the question is turned around and asks what term a certain number is
in a sequence.

1. We can
use the same logic as above to come up with an expression.

2. Find
the expression for the n^{th} term of the sequence (same as above).

3. Solve
for n: an + b = x, where x is the given number.

Ex [4] 58 is
what term in the sequence 1, 4, 7,...

a. Since
we are adding by 3, 3 should be the first number.

b. If we
subtract 2 from 3 we get 1.

c. So the
expression is 3n - 2.

d.
Solve: 3n - 2 = 58.

e. The
answer is 20.

Ex [5] 105
is what term in the sequence 9, 13, 17,...

a. Since
we are adding by 4, the first number should be 4.

b. If we
add 5 to 4 we get 9.

c. So the
expression is 4n + 5.

d.
Solve: 4n + 5 = 105.

e. The
answer is 25.

Back
to top