Math Problem Statement

The first three terms of an arithmetic progression are 12 - x, 18, and 4. Find (a) the value of x, (b) the common difference of the arithmetic progression, and (c) the sum of the 10th term to the 20th term.

Solution

The image shows a problem about an arithmetic progression, written in both Malay and English. The key details of the problem are as follows:

Problem (Arithmetic Progression):

  1. Given: The first three terms of an arithmetic progression are 12−x12 - x, 18, and 4.

  2. Tasks: a) Find xx.
    b) Determine the common difference of the arithmetic progression.
    c) Calculate the sum of the terms from the 10th term to the 20th term.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Progression
Common Difference
Sum of Terms

Formulas

Common difference: d = T2 - T1
General term of arithmetic progression: Tn = a + (n-1) * d
Sum of arithmetic series: S = (n/2) * (T1 + Tn)

Theorems

Arithmetic Progression Formula

Suitable Grade Level

Grades 9-10

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