nth Term of an Arithmetic Sequence

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ACT Math › nth Term of an Arithmetic Sequence

Questions 1 - 10

What is the th term in the following series of numbers: ?

148

Explanation

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .

What is the th term in the following series of numbers: ?

148

Explanation

Find the term of the following sequence:

$a_{10}=-111$

$a_{10}=-123$

$a_{10}=-99$

$a_{10}=-125$

$a_{10}=-113$

Explanation

The formula for finding the $n^{th}$ term of an arithmetic sequence is as follows:

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the term:

$a_{10}=-3+(-12)(10-1)$

$a_{10}=-3+(-12)(9)$

$a_{10}=-3-108$

$a_{10}=-111$

Find the term of the following sequence:

$a_{10}=-111$

$a_{10}=-123$

$a_{10}=-99$

$a_{10}=-125$

$a_{10}=-113$

Explanation

The formula for finding the $n^{th}$ term of an arithmetic sequence is as follows:

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the term:

$a_{10}=-3+(-12)(10-1)$

$a_{10}=-3+(-12)(9)$

$a_{10}=-3-108$

$a_{10}=-111$

What is the next term in the sequence?

Explanation

The difference between each term is constant, thus the sequence is an arithmetic sequence.

Simply find the difference between each term, and add it to the last term to find the next term.

$\ 15-9 = 6 \newline 15+6 = 21$

What is the next term in the sequence?

Explanation

The difference between each term is constant, thus the sequence is an arithmetic sequence.

Simply find the difference between each term, and add it to the last term to find the next term.

$\ 15-9 = 6 \newline 15+6 = 21$

What is the next term of the series ?

Explanation

Begin by looking at the transitions from number to number in this series:

From to : Add

From to : Subtract

From to : Add

From to : Subtract

From what you can tell, you can guess that the next step will be to add . Thus, the next value will be .

What is the next term of the series ?

Explanation

Begin by looking at the transitions from number to number in this series:

From to : Add

From to : Subtract

From to : Add

From to : Subtract

From what you can tell, you can guess that the next step will be to add . Thus, the next value will be .

What is the next term in the following sequence: ?

Explanation

This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two , next the fourth is equal to the sum of the second and the third , and the same continues for each element after this. Thus, the next element in the series will be equal to or .