PSAT Math Multiple-Choice Question 812: Answer and Explanation

Question: 812

n	Pattern
1	1
2	1 + 3
3	1 + 3 + 5
4	1 + 3 + 5 + 7
5	1 + 3 + 5 + 7 + 9

The table above gives the values of a sum of the first n numbers, starting with 1. Which of the following is a correct statement about n?

• A. The product of n and its corresponding sum decreases as n increases.
• B. The difference between each additional value of n and the previous value of n is increasing exponentially.
• C. The sum of the first n odd numbers equals the square of n.
• D. The sum of the first n numbers is comprised solely of prime numbers.

Correct Answer: C

Explanation:

(C) Rewrite the table by calculating the actual sums:

n	Pattern	Sum
1	1	1
2	1 + 3	4
3	1 + 3 + 5	9
4	1 + 3 + 5 + 7	16
5	1 + 3 + 5 + 7 + 9	25

Each value in the "Sum" column is the corresponding value of n squared:

1 = 1² ; 4 = 2² ; 9 = 3² ; 16 = 4² ; 25 = 5²