Question

Here are the first five terms of an arithmetic sequence.

26 19 12 5 –2

Find an expression, in terms of n, for the nth term of this sequence.

Answer 1

Step-by-step explanation:

the first term is a1 = -3 the second term is a2 =1 the increment is a2-a1 = 1-(-3) = 4 = i

so the second term comes from a2=a1+(2-1)i = 1 the third term comes from a3 = a1 + (3-1)i = 5

so the nth term will be; an = a1 + (n-1)i f.i. the 6th term will be a6 = a1 + (6-1)4 = 17

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