carmen is playing with blocks. she arranges stacks of blocks so that each successive level of blocks has 1…

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

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