carmen is playing with blocks. she arranges s...
carmen is playing with blocks. she arranges stacks of blocks so that each successive level of blocks has 1 fewer block than the level below it and the top level has 1 block. such a stack with 3 levels is shown below. carmen wants to make such a stack with 12 levels. how many blocks would she use to build this stack? (1 point) a. 66 b. 78 c. 132 d. 144 e. 156
Answer
# Explanation:
## Step1: Identify the sequence
The number of blocks in each level forms an arithmetic - sequence: 1, 2, 3, …, n. Here, n = 12.
## Step2: Use the sum formula for an arithmetic sequence
The sum formula of the first n terms of an arithmetic sequence is $S_n=\frac{n(a_1 + a_n)}{2}$, where n is the number of terms, $a_1$ is the first - term, and $a_n$ is the nth term. In this case, $a_1 = 1$, $n = 12$, and $a_n=a_{12}=12$.
## Step3: Calculate the sum
Substitute the values into the formula: $S_{12}=\frac{12\times(1 + 12)}{2}=\frac{12\times13}{2}=78$.
# Answer:
B. 78