Question 49 Answer and Explanation _ACT OG1 Form 1MC Math Section

49. Which of the following statements describes the total number of dots in the first n rows of the triangular arrangement illustrated below?

A. This total is always equal to 25 regardless of the number of rows.

B. This total is equal to twice the number of rows.

C. This total is equal to 5 times the number of rows.

D. This total is equal to the square of the number of rows.

E. There is no consistent relationship between this total and the number of rows.

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

It can be obtained from the information given in the title that for this sequence: a_n=1+2n, the sum of the first n items is: S_n=n ×1 + n(n-1)=n² , the answer is D. The sum of the first 4 columns can also be tested by exhaustive method, only the answer D is correct.