A collection of dimes is arranged in a triangular array, with 14 coins in the base row, 13 in the next, 12 in the next, and so forth. Find the value of the collection.
A) $\$ 10.50$
B) $\$ 1.05$
C) $\$ 5.25$
D) $\$ 21.00$

Question

Quizplus · Accepted Answer

The number of coins in each row forms an arithmetic sequence with a common difference of -1. The first term is 14 and the last term is 1. The sum of an arithmetic sequence is given by the formula:$$S = \frac{n}{2}(a_1 + a_n)$$where n is the number of terms, a1 is the first term, and an is the last term.In this case, n = 14, a1 = 14, and an = 1. Substituting these values into the formula, we get:$$S = \frac{14}{2}(14 + 1) = 105$$Since each coin is worth 10 cents, the value of the collection is:$$105 	imes 10 = \$10.50$$

A Collection of Dimes Is Arranged in a Triangular Array $10.50\$ 10.50$10.50

A Collection of Dimes Is Arranged in a Triangular Array $\$ 10.50$