Question

A grocery clerk sets up a display of 12-pack cartons of cola there are 15 cartons at the base of the triangle and one at the top. How many cartons are needed for the complete display?
a. 15 b. 180 c. 120 cartons d. 30 cartons

Answer 1

We have to determine the number of cartons required to complete the display of cartons.

Since, the grocery clerk displays 15 cartons at the base of the triangle and one at the top. Therefore, one carton is reduced at previous step and so on.

So, the total number of cartons at the display = 1+2+3+4+5+......+ 15

Since, this series is in arithmetic progression.

Sum of arithmetic progression upto 'n' terms with first term 'a' and last term 'l' is given by the formula $\frac{n}{2}(a+l)$

= $\frac{15}{2}(1+15)$

= $15 \times 8$

= 120

Therefore, 120 cartons are needed for the complete display.

So, Option 3 is the correct answer.