Problem Solving

Que: Suzy saves $30 per month. In each of the next 30 months, she saved $30 more than he saved in the previous month. What is the total amount she saved during the 30-month period?

(A) $900
(B) $2,800
(C) $13,950
(D) $9,300
(E) $12,000

Solution: Sum of first ‘n’ positive integers = \(\frac{n\ \cdot\ \left(n+1\right)}{2}\)

The total amount she saved during the 30-month period is $30 + 2 * $30 +…+ 29 * $30 + 30 * $30 = $30(1 + 2 + … + 29 + 30).

Since the sum of first 30 positive integers 1 + 2 + …+ 29 + 30 = \(\frac{30\ \cdot\ 31\ }{2}\) = 15 * 31 = 465, we get total amount saved in 30 months

=> $30(1+2+…+29+30) = $30 * 465 = $13,950

Therefore, C is the correct answer.

Answer C