Question

The first three terms of an arithmetic progression are 3h, k, h+2.

(a) Express k in terms of h.

(b) Find the 10th term of progression in term of h.​

Answer 1

Since the sequence is arithmetic, there is a number

d

(the "common difference") with the property that

5

k

−

2

=

(

2

k

+

3

)

+

d

and

10

k

−

15

=

(

5

k

−

2

)

+

d

. The first equation can be simplified to

3

k

−

d

=

5

and the second to

5

k

−

d

=

13

. You can now subtract the first of these last two equations from the second to get

2

k

=

8 , implying that k=4

.

Alternatively, you could have set

d=3k−5=5−13 and solved for k=4 that way instead of subtracting one equation from the other.

It's not necessary to find, but the common difference

d=3k−5=3⋅4−5=7

. The three terms in the sequence are 11, 18, 25.