Comparing Sequences and Series

Problem: 1

Give the first six terms of the sequence a_n = (n + 2)².

Problem: 3

Give the first six terms of the sequence a_n = 2ⁿ^{– 1}

Problem: 5

Give the first six terms of the sequence:

Problem: 7

Give the first six terms of the sequence:

Problem: 9

Give the first five terms of the sequence.

a₀ = –2

a_n = a_n_{– 1} – 4

Problem: 11

Give the first five terms of the sequence.

a₀ = 1

a_n = n² – a_n_{– 1}

Problem: 13

Find the pattern in the sequence 10, 12, 15, 19, 24,.... Calculate the next three terms of the sequence.

Problem: 15

Determine if the formula a_n= 2a_n_–1– 1 (where a₁= 4) is recursive or explicit.

Calculate the first five terms of the sequence.

Problem: 17

Determine if the formula a_n= 3n² – 2 is recursive or explicit. Calculate the first

five terms of the sequence.

Problem: 19

Find an explicit formula for the sequence 5, 10, 15, 20, 25,....

Calculate a₁₄.

Problem: 21

Find an explicit formula for the sequence

Calculatea_15.

Problem: 23

Find the recursive formula for the sequence 1, 4, 16, 64, 256,... Calculate the next term in the sequence.

Problem: 25

Draw the graph of the sequence:

1, 3, 5, 7, 9, 11

Problem: 27

Determine if the list 5, 30, 180, 1080, 6480, ..... is a sequence or a series. Also find if it is finite or infinite.

Problem: 29

Determine if the list is a sequence or a series. Also find if it is finite or infinite.

Problem: 31

Find the related series for the finite sequence 90, 82, 74, 66, 58, 50. Then find the sum of the series.

Problem: 33

Write the given series in the expanded form:

Problem: 35

Write the given series in the expanded form:

Problem: 37

Write the given series in the expanded form:

Problem: 39

Write the sigma notation of the given series:

3 + 6 + 9 + 12 + 15

Problem: 41

Write the series in sigma notation:

1² + 2² + 3² + .........+ 40²

Problem: 43

Write the series in sigma notation:

Problem: 45

Write the series in sigma notation:

Problem: 47

Write the sigma notation of the series:

4 – 16 + 48 – 128 + 320 – ...

Problem: 49

Find the sum of the series:

Problem: 51

Find the sum of the series:

Problem: 53

Find the sum of the series:

Problem: 55

Find the sum of the series:

Problem: 57

Find the sum of the series:

Problem: 59

Choose the correct choice:

(A) log 4¹⁵ (B) log 15⁴ (C) log 4⁵ (D) log 5⁴

Problem: 1

Give the first six terms of the sequence a_n = (n + 2)².

Problem: 3

Give the first six terms of the sequence a_n = 2ⁿ^{– 1}

Problem: 5

Give the first six terms of the sequence:

Problem: 7

Give the first six terms of the sequence:

Problem: 9

Give the first five terms of the sequence.

a₀ = –2

a_n = a_n_{– 1} – 4

Problem: 11

Give the first five terms of the sequence.

a₀ = 1

a_n = n² – a_n_{– 1}

Problem: 13

Find the pattern in the sequence 10, 12, 15, 19, 24, .... Calculate the next three terms of the sequence.

Problem: 15

Determine if the formula a_n= 2a_n_–1– 1 (where a₁= 4) is recursive or explicit.

Calculate the first five terms of the sequence.

Problem: 17

Determine if the formula a_n= 3n² – 2 is recursive or explicit. Calculate the first

five terms of the sequence.

Problem: 19

Find an explicit formula for the sequence 5, 10, 15, 20, 25, ....

Calculate a₁₄.

Problem: 21

Find an explicit formula for the sequence

Calculate a_15.

Problem: 23

Find the recursive formula for the sequence 1, 4, 16, 64, 256, ... Calculate the next term in the sequence.

Problem: 25

Draw the graph of the sequence:

1, 3, 5, 7, 9, 11

Problem: 27

Determine if the list 5, 30, 180, 1080, 6480, ..... is a sequence or a series. Also find if it is finite or infinite.

Problem: 29

Determine if the list is a sequence or a series. Also find if it is finite or infinite.

Problem: 31

Find the related series for the finite sequence 90, 82, 74, 66, 58, 50. Then find the sum of the series.

Problem: 33

Write the given series in the expanded form:

Problem: 35

Write the given series in the expanded form:

Problem: 37

Write the given series in the expanded form:

Problem: 39

Write the sigma notation of the given series:

3 + 6 + 9 + 12 + 15

Problem: 41

Write the series in sigma notation:

1² + 2² + 3² + .........+ 40²

Problem: 43

Write the series in sigma notation:

Problem: 45

Write the series in sigma notation:

Problem: 47

Write the sigma notation of the series:

4 – 16 + 48 – 128 + 320 – ...

Problem: 49

Find the sum of the series:

Problem: 51

Find the sum of the series:

Problem: 53

Find the sum of the series:

Problem: 55

Find the sum of the series:

Problem: 57

Find the sum of the series:

Problem: 59

Choose the correct choice:

(A) log 4¹⁵ (B) log 15⁴ (C) log 4⁵ (D) log 5⁴

Hotmath Practice Problems