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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

Maintaining Mathematical Proficiency

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Exercise 8 Page 271

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.

a_n=2n+10

Practice makes perfect

Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+( n-1) dIn 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 nth term in the sequence. For this exercise, the first term is a_1= 12. Let's observe the other terms to determine the common difference d. 12+2 →14+2 →16+2 →18... 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

d= 2, a_1= 12

a_n= 12+(n-1)( 2)

Distribute 2

a_n=12+2n-2

Subtract term

a_n=2n+10

The equation for the nth term of the given arithmetic sequence is a_n=2n+10.

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Exercises p.271