REVIEW FOR MATH 10 1ST QUARTER

____ is an enumerated collection of objects in which repetitions are allowed and order matters, it also follow a particular pattern or rule

• Sequence

• Number

• Term

• Sets

A sequence having specific first and last terms.

• Continuous

• Infinite

• Finite

• none of the choices

The common difference of arithmetic is always positive.

• TRUE

• FALSE

Answer explanation

COMMON DIFFERENCE CAN BE POSITIVE AND NEGATIVE OR NEITHER

E.g.

{2, 2, 2, 2} d=0

{10. 5, 0} d=-5

{1, 3, 5, 7} d=2

The common difference of an arithmetic sequence is equal to the difference of any of its two terms.

• TRUE

• FALSE

Answer explanation

The common difference determined by subtracting the preceding term from any term.

If the first term of the sequence is 4 and the second term is X+3, what should be the next term if it is an arithmetic sequence?

• X+6

• 2X+2

• 2X+6

• My brain is not working

Answer explanation

to get the common difference subtract the first term from the second term

first term: 4

Second term: X+3

d = X+3 - 4

d = X-1

then add the common difference from 2nd term

Second term: X+3

X+3 + X-1 = 2X+2

What is the arithmetic mean of 5 and 65

In an arithmetic sequence, if the sum of the first 10 terms is equal to the sum of the next 10 terms, then the common difference must be zero.

• True

• FALSE

Answer explanation

If the common difference is zero then all term are the same, therefore the sum of first 10 terms is equal to the sum of next 10 term.

Identify the type of the sequence:
   {4, 4+x, 4+2x, 4+3x, ...}

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Answer explanation

it is arithmetic since it has common difference (d) = x

Identify the type of the sequence:
   {5+x, 10+2x, 20+4x ...}

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Answer explanation

it is geometric since it has common ratio equal to 2

• Arithmetic

• Geometric

• Fibonacci

• Harmonic

Answer explanation

it is harmonic since the reciprocal of the term represent arithmetic and it has common difference equal to 6