Exercise 23 Page 319

Can we find the common difference and the first term just by looking at the recursive formula?

a_n=3n-6

Practice makes perfect

The explicit formula of an arithmetic sequence combines the information provided by the two equations of the recursive form into a single equation. Recursive: a_n&=a_(n-1)+ d; a_1&= a_1 [0.8em] Explicit: a_n&= a_1+(n-1) d In these formulas, d is the common difference and a_1 is the first term. Looking at the given recursive formula, we can identify the common difference d and the value of the first term a_1. a_n=a_(n-1)+ 3, a_1= - 3 We can see that 3 is the common difference and the first term is - 3. Now we have enough information to form an explicit formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

a_1= - 3, d= 3

a_n= - 3+(n-1) 1II3

Distr

Distribute 3

a_n = - 3 + 3n - 3

SubTerms

Subtract terms

a_n = 3n - 6

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