Sequence Worksheets

1Calculate the nth term of the following sequences:

8, 3, −2, −7, −12, ...

3, 6, 12, 24, 48, ...

4, 9, 16, 25, 36, 49, ...

5, 10, 17, 26, 37, 50, ...

6, 11, 18, 27, 38, 51, ...

3, 8, 15, 24, 35, 48, ...

−4, 9, −16, 25, −36, 49, ...

4, −9, 16, −25, 36, −49, ...

2/4, 5/9, 8/16, 11/25, 14/36,...

10  Calculating the nth Term

2Calculate the nth term of the following sequences:

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

Calculating the nth Term

10 Calculating the nth Term

11  Calculating the nth Term


1

Calculate the nth term of the following sequences:

8, 3, −2, −7, −12, ...

3 − 8 = −5.

−2 − 3 = −5.

−7 − (−2) = −5.

−12 − (−7) = −5.

d = −5.

an = 8 + (n − 1) (−5) = 8 −5n +5 = −5n + 13


3, 6, 12, 24, 48, ...

6/3 = 2.

12/6 = 2.

24/12 = 2.

48/24 = 2.

r = 2.

an = 3 · 2 n−1


4, 9, 16, 25, 36, 49, ...

22, 32, 42, 52, 62, 72, ...

bn = 2 + (n − 1) · 1 = 2 + n − 1 = n + 1

an = (n + 1)2


5, 10, 17, 26, 37, 50, ...

22 + 1 , 32 + 1, 42 +1, 52 + 1, 62 + 1 , 72 + 1, ...

an = (n + 1) 2 + 1


6, 11, 18, 27, 38, 51, ...

22 + 2 , 32 + 2, 42 + 1, 52 + 2, 62 + 2 , 72 + 2, ...

an = (n + 1)2 − 1


3, 8, 15, 24, 35, 48, ...

22 − 1 , 32 − 1, 42 − 1, 52 − 1, 62 − 1 , 72 − 1, ...

an = (n + 1)2 − 1

2, 7, 14, 23, 34, 47, ...

22 − 2 , 32 − 2, 42 − 2, 52 − 2, 62 − 2 , 72 − 2, ...

an = (n + 1) 2 − 2


−4, 9, −16, 25, −36, 49, ...

an = (−1)n (n + 1)2


4, −9, 16, −25, 36, −49, ...

an = (−1)n−1 (n + 1)2


2/4, 5/9, 8/16, 11/25, 14/36,...

There are two sequences:

2, 5, 8, 11, 14, ...

4, 9, 16, 25, 36, ...

The first is an arithmetic sequence with d = 3. The second is a sequence of square numbers.

an = (3n − 1)/(n + 1)2


10  Calculating the nth Term

If the sign is ignored, the numerator is an arithmetic sequence with d = 2.

The denominator is an arithmetic sequence with d = 1.

Since the odd terms are negative, multiply by (−1)n.

The nth Term of a Sequence


2

Calculate the nth term of the following sequences:

The nth Term of a Sequence

The numerator is constant.

The denominator is an arithmetic sequence with d = 1.

The nth Term of a Sequence


The nth Term of a Sequence

The numerator is an arithmetic sequence with d = 1.

The denominator is an arithmetic sequence with d = 1.

The nth Term of a Sequence


The nth Term of a Sequence

For this sequence, simplify some of the fractions.

Sequence

The numerator is an arithmetic sequence with d = 1.

The denominator is an arithmetic sequence with d = 1.

The nth Term of a Sequence


The nth Term of a Sequence

If the sign is ignored, it is an arithmetic sequence with d = 1.

Since the odd terms are negative, multiply by (−1)n.

The nth Term of a Sequence


The nth Term of a Sequence

Sequence

If the sign is ignored, the numerator is an arithmetic sequence with d= 1.

The denominator is an arithmetic sequence with d = 1.

Since the even terms are negative, multiply by (−1)n+1.

The nth Term of a Sequence


The nth Term of a Sequence

It is an oscillating sequence.

The odd terms are an arithmetic sequence with d = 1.

The denominator of the terms form an arithmetic sequence with d = 1.

The nth Term of a Sequence


The nth Term of a Sequence

Sequence

If the sign and the exponent is ignored, there is an arithmetic sequence with d = 1.

Since the terms are to the square, raise the general term to the square.

Since the terms are squared, the nth term has to be squared.

Since the odd terms are negative, multiply by (−1)n.

The nth Term of a Sequence


The nth Term of a Sequence

Sequence

The numerator of the odd terms form an arithmetic sequence with d = 1.

Since the terms are to the square, raise the general term to the square.

The first term in the denominator (ignoring the square) is an arithmetic sequence with d = 1 (not counting the terms pairs).

The nth Term of a Sequence


The nth Term of a Sequence

The numerator is an arithmetic sequence with d = 2.

The denominator is a geometric sequence with r = 2.

The nth Term of a Sequence


10 The nth Term of a Sequence

If the sign is ignored, the numerator is an arithmetic sequence with d = 1.

The denominator is a geometric sequence with r = 3.

Since the even terms are negative, multiply by (−1)n+1.

The nth Term of a Sequence




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