Question

Difference of first terms of two arithmetic sequences with same common difference is 10. (a) What is
the difference between second term of these sequences?
(b) What is the difference between nth term of these sequences?
(c) Find the difference between the sum of first n terms these sequences

Answer 1

Answer:

First term of the sequence is 10 and common difference is 3.

a

1

= 10 and d = 3

Next term = a

2

=a

1

+d=10+3=13

a

3

=a

2

+d=13+3=16

Thus, first three terms of the sequence are 10, 13 and 16.

Let 100 be the nth term of the sequence.

a

n

=a

1

+(n−1)d

100=10+(n−1)3

90=(n−1)3

n−1=30

n=31, which is a whole number.

Therefore, 100 is the 31

st

term of the sequence.