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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 10 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=- 7n+29

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= 22. Let's observe the other terms to determine the common difference d. 22- 7 →15- 7 →8- 7 → 1 ... 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= - 7, a_1= 22

a_n= 22+(n-1)( - 7)

Distribute - 7

a_n=22-7n+7

Add terms

a_n=- 7n+29

The equation for the nth term of the given arithmetic sequence is a_n=- 7n+29.

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Exercises p.271