Question

The algebra of an arithmetic sequence is x

n

= 3n+2.

a) Write its first term and common difference.

b) What is the remainder on dividing each term of this sequence by 3.

c) Is 100, a term in this sequence? Why?​

Answer 1

Answer:

n=3n+2

a)n=1;

3n+2=3 x 1+2

=3+2

=5

first term =5

if n=2

3 X 2 + 2

=8

a+d=8

5+d=8

d=8-5

=3

common difference=3

b) n=3n+2

therefore remainder = 2

c) a+(n-1)d =100

5+(n-1)3 =100

(n-1)3 =100-5

3n-3 =95

3n =95+3

=98

n=98/3

= 32. 2/3

n. cannot be a fraction therefore 100 is not a term in the series