Math Problem Statement

A series of math problems related to arithmetic and geometric sequences, focusing on recruitment trends, bacterial growth, cable lengths, and summation of a series.

Solution

I see the questions provided in the image pertain to sequences and series (Arithmetic and Geometric Progressions). Let’s go through them step by step to find solutions:


Question 7

Recruitment in a shoe factory follows an arithmetic sequence. January: 200 employees, February: 240 employees, March: 280 employees, etc. Find the total recruitment for one year.

  1. Identifying the sequence:
    The first term a=200a = 200, the common difference d=240200=40d = 240 - 200 = 40.

  2. **

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic Progression
Geometric Progression
Exponential Growth
Summation of Series

Formulas

Sum of Arithmetic Series: S_n = n/2 * (2a + (n-1)d)
Sum of Geometric Series: S_n = a * (r^n - 1) / (r - 1)
Exponential Growth Formula: N_t = N_0 * 2^(t/T)

Theorems

Properties of Arithmetic and Geometric Sequences
Exponential Growth in Bacteria Doubling

Suitable Grade Level

Grades 9-10