What is the general term equation, an, for the arithmetic sequence 5, 1, −3, −7, . . . , and what is the 21st term of this sequence?

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18-10-2017
Mathematics

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What is the general term equation, an, for the arithmetic sequence 5, 1, −3, −7, . . . , and what is the 21st term of this sequence?

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altavistard altavistard · Answer 1 · 2017-10-18T18:18:24+02:00

altavistard altavistard

18-10-2017

The general term is obtained by starting with the initial value 5 and then subtracting 4 each time you wish to generate a new term:

a2 = second term = 5+(2-1)(-4) = 5+(-4) = 1

General term:

an = nth term = 5+(n-1)(-4)

Thus, the 21st term is 5+(21-1)(-4) = 5 + (20)(-4) = -75 (answer)

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