Application of Arithmetic Sequence and Series
Example:
Tickets for a certain show were printed bearing numbers from to
. The odd number tickets were sold by receiving cents equal to thrice the number on the ticket while the even number tickets were issued by receiving cents equal to twice the number on the ticket. How much was received by the issuing agency?
Solution:
Let and
be the amounts received for odd number and even number tickets respectively, then
and
Thus,
there are
terms in each series
Hence the total amount received by the issuing agency cents
Example:
A clock strikes once when its hour hand is at , twice when it is at
and so on. How many times does the clock strike in six hours?
Solution:
Since the clock strikes once when its hour hand is at , twice when it is at
and so on, so the sequence of strikes from
hour to
hours is
.
Here ,
,
so
This shows that the clock strikes times in
hours.
Example:
A factory owner repays his loan of by
in the first monthly installment and then increases the payment by
in every installment. How many installments will it take for him to clear his loan?
Solution:
By the given conditions, we have
,
,


