Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
6. Arithmetic Sequences
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Exercise 8 Page 212

What is the first term of the sequence? What is the common difference between terms? Use these values in the explicit equation for arithmetic sequences.

Equation: a_n=n+3
Value of a_(25): 28

Practice makes perfect
Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+( n-1) d In this form, a_1 is the first term in a given sequence, d is the common difference from one term to the next, and a_n is the {\color{#FF0000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 4. Let's observe the other terms to determine the common difference d. 4+1 →5+1 →6+1 →7... By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.
a_n=a_1+(n-1)d
a_n= 4+(n-1)( 1)
a_n=4+n-1
a_n=n+3
This equation can be used to find any term in the given sequence. To find a_(25), the {\color{#FF0000}{25}}^\text{th} term in the sequence, we substitute 25 for n.
a_n=n+3
a_(25)= 25+3
a_(25)=28
The 25^\text{th} term in the sequence is 28.

Extra

More About Sequences

There is a lot of helpful information about arithmetic sequences available in our original course content!

Another common type of sequence is a geometric sequence, which has a common ratio instead of a common difference — the consecutive numbers are multiplied by the same number each time instead of having the same number added to them.