Arithmetic and Geometric Series Discrete Review

Arithmetic and Geometric Series

Multiple Choice

Which of the following sequences is finite?

• 2, 4, 6, 8, ...

• 3, 7, 11, 15, 19

• 10, -20, 40, -80, ...

• All of the sequences are finite.

Math Response

To find the sum of an ARITHMETIC series we use the formula $$S_n\ =\ \frac{n}{2}\left(a_1+a_n\right)$$  where n is the number of terms in the sequence, a_1 is the first term and a_n is the last term.

Find the value of first 100 terms of:  $$3+10+17+24+31+38\ ...$$  using the formula. 

Type answer here

Correct Answer: 34950

Deg^°

Rad

Multiple Choice

Given the series $$4+9+14+19+...+99$$  

what term number (n) is 99?

Hint - use  $$a_n=a_1+\left(n-1\right)d$$  

• 19

• 21

• 20

• 22

Math Response

$$4+9+14+19+...+99$$  

Find the sum of the series given that 99 is the 20th term.

$$S_n=\frac{n}{2}\left(a_1+a_n\right)$$  

Type answer here

Correct Answer: 1030

Deg^°

Rad

Fill in the Blank

To find a GEOMETRIC series, you must use the formula $$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$  

Find the sum of the first 8 terms of the series  $$2+4+8+...$$  

Multiple Choice

What is the sum of the series $$100+20+4+\frac{4}{5}+\frac{4}{25}+\frac{4}{125}$$ ?

$$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$  

• 100

• 128

• 124.992

• 390.600

Multiple Choice

Given the series  $$7+14+28+...+896$$  What term is 896?

Use  $$a_n=a_1\cdot r^{\left(n-1\right)}$$  

• 5

• 6

• 7

• 8

Fill in the Blank

What is the sum of $$7+14+28+...+896$$ ? 

$$S_n=\frac{a_1\left(1-r^n\right)}{1-r}$$   

Sigma Notation

Fill in the Blank

$$\sum_{n=1}^{12}3x-10$$  

Find the sum of the arithmetic series.

HINT - find a_1, a_n, and n.  Then use  $$S_n=\frac{n}{2}\left(a_1+a_n\right)$$  

Multiple Choice

Which is the correct summation notation for $$5+10+20+40+80+160+320$$  ?

• $$\sum_{n=1}^75\left(2\right)^{\left(n-1\right)}$$  

• $$\sum_{n=1}^8\left(5\left(2\right)^{\left(n-1\right)}\right)$$  

• $$\sum_{n=1}^72\left(5\right)^{\left(n-1\right)}$$  

• $$\sum_{n=1}^62\left(5\right)^n$$  

Fill in the Blank

$$\sum_{n=1}^82\left(3\right)^{\left(n-1\right)}$$  

Find the sum of the series