Sequences and Series Review

REVIEW:
SEQUENCES & SERIES

ARITHMETIC/GEOMETRIC/HARMONIC/FIBONACCI

COVERAGE

• Arithmetic (Common difference, nth term and Series)

• Geometric (Nth term and series)

• Harmonic (common difference & nth term)

• Fibonacci (golden rat

Multiple Choice

The difference between any two consecutive terms is constant.

• Arithmetic Sequence

• Geometric Sequence 

• Harmonic Sequence

• Fibonacci Sequence

Multiple Choice

A sequence in which each term is obtained by multiplying the preceding term by a common ratio.

• Arithmetic Sequence

• Geometric Sequence 

• Arithmetic Series

• Geometric Series

Multiple Choice

The sequence formed by the reciprocals of the terms of an arithmetic sequence.

• Arithmetic Sequence 

• Geometric Sequence 

• Harmonic Sequence

• Fibonacci Sequence

Multiple Choice

The sequence formed by the reciprocals of the terms of an arithmetic sequence.

• Arithmetic Sequence

• Geometric Sequence 

• Harmonic Sequence

• Fibonacci Sequence

Multiple Choice

Its formula is used to find the nth term of harmonic sequence.

• Arithmetic Sequence 

• Geometric Sequence

• Harmonic Sequence

• Fibonacci Sequence

Open Ended

THE VALUE OF PHI OR GOLDEN RATIO (UP TO 6

Multiple Choice

These sequences involve the four fundamental operations in finding the next term.

• Arithmetic & Harmonic           

• Geometric & Fibonacci

• Harmonic & Fibonacci

• Arithmetic & Geometric

COMPREHENSION

Multiple Choice

Let a, b and c are three consecutive terms of an arithmetic sequence. Which of the following is a true statement?

• $$a+c=b$$

• $$\frac{a+c}{4}=b$$

• $$\frac{a+c}{2}=b$$

• $$a+c=\frac{b}{2}$$

Multiple Choice

Which is an example of an arithmetic sequence?

• 5 ,7 ,9 ,11 ,14 …

• -2, 1 ,6 ,8, 10…

• C. -15, -11, -7, -3…

• ½, 3/4 , 1, 5/4, 2/3…

Multiple Choice

How to get the common ratio of geometric sequence?

• Divide the first term to the second term.       

• Multiply the second term to the first term.

• Divide the second term to the first term.

• Subtract the second term to the first term

Multiple Choice

How will you differentiate geometric sequence from arithmetic sequence?

• Geometric sequence is finite while arithmetic sequence is infinite.

• Geometric sequence involves division and multiplication while arithmetic sequence involves subtraction and addition.

• Geometric sequence is much easier to find the means than arithmetic.

• Geometric sequence has a common difference while arithmetic sequence has common ratio.

Multiple Choice

Which among the steps is NOT true in illustrating geometric sequence?    

• Divide the succeeding term to the previous term.

• Multiply the common ratio to find the next term of the sequence.

• Divide the common ratio to find the next term of the sequence.

• If we add the first and third term divided by two, the answer is the second term.

Multiple Choice

Which among the steps is NOT true in determining the nth term of harmonic sequence?

• Get the reciprocals of terms before finding the common difference.

• Use the formula of arithmetic sequence to find the nth term.

• Like in arithmetic sequence, add the preceding term to the previous term to find the common difference.

• Get the reciprocal of the final answer.

Multiple Choice

Which sequence is NOT arithmetic?

• 2, 4, 6, 8, 10...

• 3, 6, 9, 12, 15 ...

• 63, 67, 71, 76 …

• ½, ¾, 1, 5/4…  

Multiple Choice

Which sequence is NOT geometric?

• 1, 11, 21, 31…

• 1, 2, 4, 16, 32…

• 1, -2, 4, -8, 16…

• 1, 2, 3, 4, 5, 6…

ANALYSIS

Multiple Choice

The common ratio of geometric sequence may be written as a ratio or rational.

• 80, 20, 5…  

• 5, 30, 180…

• Both are correct

• None of the choices are correct

Multiple Choice

In arithmetic sequence, the difference is constant.

• 12, 24, 36, 48, 60…   

• 5, 15, 25, 35, 45…

• Both are correct

• None of the choices

Multiple Choice

These sequences are closely related as they both have the same first term, but you can see how different they become if they have a common difference or a common ratio.

• We can create a decreasing arithmetic sequence by choosing a negative common difference.

• Decreasing geometric sequence would have a common ratio of less than 1. 

• BOTH ARE CORRECT

• NONE OF THE CHOICES ARE CORRECT