52. a sequence is defined recursively by a1 = 9 and an = an - 1-(n - 1)^2 for positive integers n≥2. if a11…

52. a sequence is defined recursively by a1 = 9 and an = an - 1-(n - 1)^2 for positive integers n≥2. if a11 = - 376, what is a12? f. - 497 g. - 476 h. - 387 j. - 376 k. - 110 53. a teacher is researching the number of students at her school that are interested in a chess club. of the 865 students at her school, she asks 130 randomly selected students if they would agree to be interviewed. of the 130 students she asks, 90 students agree to be interviewed, and 40 students decline. the teacher finds that 83 of those students interviewed are interested in a chess club. what is the target population that her random sample is meant to represent? a. the 865 students at the teacher’s school b. the 40 students that declined the interview c. the 130 students the teacher asked to interview d. the 83 students that were interested in a chess club e. the 90 students that agreed to be interviewed by the teacher

52. a sequence is defined recursively by a1 = 9 and an = an - 1-(n - 1)^2 for positive integers n≥2. if a11 = - 376, what is a12? f. - 497 g. - 476 h. - 387 j. - 376 k. - 110 53. a teacher is researching the number of students at her school that are interested in a chess club. of the 865 students at her school, she asks 130 randomly selected students if they would agree to be interviewed. of the 130 students she asks, 90 students agree to be interviewed, and 40 students decline. the teacher finds that 83 of those students interviewed are interested in a chess club. what is the target population that her random sample is meant to represent? a. the 865 students at the teacher’s school b. the 40 students that declined the interview c. the 130 students the teacher asked to interview d. the 83 students that were interested in a chess club e. the 90 students that agreed to be interviewed by the teacher

Answer

52.

Explanation:

Step1: Identify the recursive formula

The recursive formula is $a_{n}=a_{n - 1}-(n - 1)^{2}$ for $n\geq2$.

Step2: Find $a_{12}$ using $a_{11}$

We know $n = 12$, so substituting into the formula gives $a_{12}=a_{11}-(12 - 1)^{2}$. Since $a_{11}=-376$, then $a_{12}=-376-11^{2}$.

Step3: Calculate the value

$a_{12}=-376 - 121=-497$.

Answer:

F. -497

53.

Brief Explanations:

The target - population is the group that the sample is meant to represent. Here, the teacher is researching the number of students at her school interested in a chess club. She randomly selects 130 students out of 865 students at her school. The 865 students at the school are the target population.

Answer:

A. The 865 students at the teacher’s school