Question

If the 13th term in a linear sequence is 92 and the 28th term in the sequence is

152, what is the 6th term in the sequence?

Answer 1

64

Explanation:

As the sequence is linear the rate of increase stays constant as we can see from the formula:
`S_n=mn+i` so it increases by m every term. In this all we do is subtract 13 from 28 to find the number of terms in between:

28-13=15

now we find the difference between 152 and 92

152-92=60

now we divide 60 and 15

60÷15=4

So M is 4 meaning every term has a difference of 4.

So now we can subtract 6 from 13:

13-6=7

Then multiply the difference per term (4) by 7

4×7=28

Finally we subtract 28 from 92 (13th terms value)

92-28=64