Which is a recursion formula for the sequence shown?

A f(n) = f(n -1) + 4

B f(n) = 4n -2

C f(n) = 2 + (n -1)(4)

D f(1) = 2, f(n) = f(n-1) + 4

Which expressions represent the missing terms in the binomial expansion shown?

\displaystyle (x + y)^7 = x^7 + 7x^6y + ... + 35x^4y^ + 35x^3 y^4 + 21x^2y^5+ ... + y^7

A 21y^5x^2, 7yx^6

B 21x^5y^2, 7xy^6

C -21x^5y^2, - 7xy^6

D x^5y^2, xy^6

What is the formula for the general term of an arithmetic sequence with a = 8 and d=2?

A t_n = 2+ (n + 1)(8)

B 8 + (n -1)(2)

C 8 + (n + 1)(2)

D 2 + (n - 1)(8)

What are the first three terms of a geometric sequence with a = 3 and r = 2?

A 3, 5, 7

B 2, 6, 18

C 3, 6, 12

D 2, 5, 8

Which series is neither arithmetic nor geometric?

A 5+15+21+27+...

B 1+8+27+64+...

C 64-32+16+-8+...

D -3-2.7-2.4-2.1-...

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = 9 - 5n

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = 2n^2 + 3n -4

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = \frac{1}{8}(4)^{n -1}

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = 0.2n + 0.8

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = \frac{n + 4}{2}

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = -3(2)^n

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

Write an explicit formula and recursive formula for the sequence.

\displaystyle -20, -17, -14, -11, ...

Write an explicit formula and recursive formula for the sequence.

\displaystyle -4000, 1000, -250, 62.5, ...

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

Write an explicit formula and recursive formula for the sequence.

\displaystyle -3, -6, -12, -24, ...

Write an explicit formula and recursive formula for the sequence.

\displaystyle -12\sqrt{2}, -10\sqrt{2}, -8\sqrt{2}, -6\sqrt{2}, ...

Write t_{11} for each sequence.

6, 10, 14, 18, ...

Write t_{11} for each sequence.

-3, -6, -12, -24, ...

Write t_{11} for each sequence.

5, -10, 20, -40, ...

Write t_{11} for each sequence.

-5, -10, -15, -20, ...

Given the explicit formula, write t_{15} for the sequence.

\displaystyle f(n) = 2(-3)^{n + 1}

Given the explicit formula, write t_{15} for the sequence.

\displaystyle t_n = 25n + 50

Given the explicit formula, write t_{15} for the sequence.

\displaystyle t_n = 25n + 50

Given the explicit formula, write t_{15} for the sequence.

\displaystyle f(n) = \frac{-3n}{4}

Determine the number of terms in each sequence.

5, 8, 11, ..., 62

Determine the number of terms in each sequence.

-4, 12, -36, ..., -19 131 876

A new lake is being excavated. One day, 1.6 t of material is removed from the lake bed. On each of 10 days after that, 5% more is removed.

(a) Write the first three excavation amounts as a sequence.

(b) Write a recursion formula to represent the amount removed each day. Use this to determine the amount removed on the fifth day.

Determine the specified sum for the series.

S_{10} for 200 + 100 + 50 + ...

Determine the specified sum for the series.

S_{18} for 12+ 5 -2 + ...$`

Determine the specified sum for the series.

120 + 110 + 100+ ... - 250

Determine the specified sum for the series.

8 + 24 + 40 + ... + 280

Determine the sum of the geometric series.

\displaystyle \frac{2}{81} + \frac{4}{27} + \frac{8}{9}+ ... + 6912

Determine the sum of the geometric series.

\displaystyle 5 + 10 + 20 + ... + 2560

Use Pascal's triangle to help you expand the expression.

(b - 3)^5

Use Pascal's triangle to help you expand the expression.

(2x - 5y)^6

The sum of the first three terms of a series is 32. Determine the fourth term if the sum of the first four terms is 40

The sum of the first three terms of a series is 32. Determine the fourth term if the sum of the first four terms is 25

Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92.

Which is greater, A or B? Explain your reasoning.

A = 50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 - 1^2 B = 50 +49 + 48+ 47+ ... + 2 + 1

In the arrangement of letters shown, starting from the top, proceed to the row below by moving diagonally to the immediate right or left. Determine the number of different paths that will spell the name PASCAL.

A new wood stain loses 6.5% of its colour every year in a city that experiences a lot of hot, sunny days. What percent of colour will a fence in this city have 6 years after being stained?

In an arithmetic series, the 4th term is 62 and the 14th term is 122. Determine the sum of the first 30 terms.

A sailboat worth $140 000 depreciates 18% in the first year and 10% every year after that. How much will it be worth 8 years after it is bought?

A magic square is an arrangement of numbers in which all rows, columns, and diagonals have the same sum. Using the magic square shown, substitute each number with the corresponding term from the Fibonacci sequence.

Show that the sum of the products of the rows is equal to the sum of the products of the columns.