Arithmetic Series and Sequences

Sequence Notation

100

What is 12! divided by 4!

19,958,400

200

Write down the first 5 terms for the sequence. 

a_n={5n-25}

{-20,-15, -10, -5, 0}

300

The given pattern continues. Write down the nth term of the sequence {a_n} suggested by the pattern:

1, -2, 3, -4, 5, -6,....

a_n=(-1)^n-1(n)

400

If a₁=5 and a₂=2 and a_n= 3a_n-1 + 2a_n-2 then find the value of a₄.

52

500

If a₁=0, a₂=3 and a_n=2a_n-1 - a_n-2 the find the value of a₅.

12

Sigma Notation

100

What is the sum in summation notation:

4+8+12+....+32

Σ⁸_k=1(4k)

200

Write out the sum: (First 3 terms to the last term)

Σ²⁵_k=1(k²-25)

(-24,-21,-16,.....,600)

300

Find the sum of the sequence:

Σ⁵⁰_k=1 18

900

400

Using the Properties of sequences, what is another way to write:

Σ ⁿ_k=1(a_k+b_k)

Σ ⁿ_k=1a_k + Σ ⁿ_k=1b_k

500

Find the sum of the sequence: 

Σ³¹_k=1(5k+25)

3255

Write the Formula

100

What is the most simplified explicit formula for the arithmetic sequence: 2, 6, 10, 14, 18.......

What is an=4n-2

200

What is the most simplified explicit formula for the arithmetic sequence: -1, 2, 5, 8, 11

What is an=3n-4

300

Find the most simplified explicit formula of the sequence 3, -2, -7, -12…

-5n+8

400

Find the most simplified explicit formula for the sequence: -16, -25, -34, -43, -52 Find the value of the tenth term

What is an=-7-9n, a10=-97

500

If a sequence has a first term of a₁=12 and a common difference d=−7. Write the formula that describes this sequence. Use the formula of the arithmetic sequence.

a_n=-7n+19

Arithmetic Sequences

100

Find the first 5 terms of the arithmetic sequence, and the common difference. 

a_n={4n-5}

{-1,3,7,11,15}

d=4

200

What is the general formula for the n^th term of an Arithmetic Sequence?

a_n=a₁+(n-1)d

300

Find the first term and the common difference of the Arithmetic Sequence described. Also, find the formula for the n^th term.

5^th term is 34

14^th term is -56

d=-10

a₁=74

a_n=-10n+84

400

A water tank develops a leak. Each week, the tank loses 5 gallons of water due to the leak. Initially, the tank is full and contains 1500 gallons. How many gallons are in the tank 20 weeks later?

1400

500

Suppose that you and other students in your school participate in a fundraising event that is trying to raise money for "underprivileged" children . The school starts with $2000 in donations. Then, each student must raise at least $45 in pledges. What is the maximum number of students needed to raise $6050.

91 Students

Arithmetic Sums

100

What is the formula for the sum of the first n terms for an arithmetic sequence?

(n/2) [a₁ + a_n]

200

Find the sum of the first 40 terms of the arithmetic series
2+5+8+11+....

2420

300

Find the sum:

Σ ⁵⁰_k=1(3k+2)

3925

400

There is a stack of logs in the backyard. There are 15 logs in the 1st layer, 14 in the second, 13 in the third, 12 in the fourth, and so on with the last layer having one log. How many logs are in the stack?

120

500

A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of 97 bricks. Each row must be decreased by 2 bricks on each end  and the construction should stop at 25th row. How many bricks does he need to buy ?

1225 bricks.