Mr. Vold is a sadistic teacher who likes writing lots of exam questions. He usually starts out the semester with only 10 questions on the first exam, but for each subsequent exam he writes one and a half as many questions as were on the previous exam! Since there's no such thing as half a question and Mr. Vold likes writing questions, round your answers up to the next integer.

(a) How many questions are on the second exam of the semester?

(b) How many questions are on the third exam of the semester?

(c) How many questions are on the fifth exam of the semester?

(d) If Mr. Vold wrote 20 exams in a semester, how many total exam questions would they have all together?

Answer

The question says for each exam Mr. Vold writes "half again as many questions as were on the previous exam."

This means the number of questions for an exam is

or

(a) The first exam had 10 questions. The second exam has

questions.

(b) The third exam has

which rounds up to 23 questions.

(c) There are (at least) two ways to interpret this question, depending on when we deal with rounding.

In part (b) we found that there were 23 questions on the third exam. In this case there are

which rounds up to 35 questions on the fourth exam.

Then there are

which rounds up to 53 questions on the fifth exam.

We could leave the rounding until the end, instead. If the first exam has 10 questions then the second exam has

the third exam has

and the fifth exam has

This rounds up to 51 questions on the fifth exam.

(d) For this question we don't want to deal with partial rounding. We're looking at a geometric series with *a* = 10 and . To find how many questions Mr. Vold writes over 20 exams we need to add up the first 20 terms of this geometric series:

Rounding up, we see Mr. Vold will write 66486 questions over the semester.