Consider the sequence 1, 7, 13, 19, . . . , 6n + 7. (a) How many terms are there in the sequence? Your answer will be in terms of n. (b) What is the second-to-last term? (c) Find the sum of all the terms in the sequence, in terms of n.

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Chapter1: Functions And Models
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Consider the sequence 1, 7, 13, 19, . . . , 6n + 7.

(a) How many terms are there in the sequence? Your answer will be in terms of n.

(b) What is the second-to-last term?

(c) Find the sum of all the terms in the sequence, in terms of n.

 

Answer the ques most simplly way

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2.2.4.
(a) n + 2 terms, since to get 1 using the formula 6n + 7 we must use
n = −1. Thus we have n terms, plus two, when n = 0 and n = -1.
SELECTED SOLUTIONS
359
(b) 6n + 1, which is 6 less than 6n + 7 (or plug in n − 1 for n).
(c) (6n+8)(n+2). Reverse and add. Each sum gives the constant 6n + 8 and
there are n + 2 terms.
Transcribed Image Text:2.2.4. (a) n + 2 terms, since to get 1 using the formula 6n + 7 we must use n = −1. Thus we have n terms, plus two, when n = 0 and n = -1. SELECTED SOLUTIONS 359 (b) 6n + 1, which is 6 less than 6n + 7 (or plug in n − 1 for n). (c) (6n+8)(n+2). Reverse and add. Each sum gives the constant 6n + 8 and there are n + 2 terms.
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