Exercise 5 Page 325

Let's analyze the given table and calculate the differences between consecutive terms in the sequence.

Since each term is larger than the previous one by 14, the given sequence is arithmetic and its common difference is d= 14. First, we will write a recursive rule for an arithmetic sequence. To do this, we have to give the value of the first term, a_1, and write a_n=a_(n-1)+ d. In our case, a_1= - 6 and d= 14. Recursive rule: a_1= - 6, a_n=a_(n-1)+ 14 Now, let's use the explicit rule of arithmetic sequences. a_n= a_1+(n-1) d Now, we will substitute known values into the explicit rule and find it.

a_n= a_1+(n-1) d

SubstituteII

a_1= - 6, d= 14

a_n= - 6+(n-1)( 14)

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Simplify right-hand side

Distr

Distribute 14

a_n=- 6+n(14)-1(14)

Multiply

Multiply

a_n=- 6+14n-14

SubTerms

Subtract terms

a_n=14n-20