Math (A Level): Sequences Help?

the difference of the sequence is -3

you first get a generic formula as a(n) = a1 - 3*n

first term is a1 = 85

10 th term is a1 - 3*(10-1) = 85 - 27 = 58

when a1-3*(n-1) < 0, you get a1 < 3n - 3 or n > 85+3 / 3 = 88/3 = 29

so from 30th term the sequence will become negative, meaning it has 29 positive terms

a(30) = 85 - 3*29 = -2

a(29) = 1

Questions 9 and 10 refer to the arithmetic sequence 85, 82, 79, …

9) The 10th term of the sequence is 85 + (10 -- 1)(82 -- 85) = 58

(a) 112

(b) 55

(c) 115

(d) 58 is the answer

(e) I don’t know

10) The number of positive terms in the sequence is given by 85/3 = 28 1/3 hence 29 terms are +ve

confeirm it term 29 = 85 + 28(--3) = 1 and next 30th term is --2

(a) 27

(b) 28

(c) 29 is the naswer

(d) 26

(e) I don’t know

The sequence begins at 85 and counts down, but like most sequences (unless otherwise defined), it is infinite. That means it will continue in that pattern beyond "0".

Number 10 is asking you how many "positive terms" (numbers above 0) are there in this sequence.

If you successfully worked out #9, all you have to do is continue to work that out until you go to 0.

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