Question
\( \begin{array}{c}2 \\ \text { Ssctron A } \\ 40 \text { markst }\end{array} \) \[ \begin{array}{l}\text { Answer all the questions in this section. All questions carry equal marks. }\end{array} \] 1. The first three terms of an Arithmetic Progression (A.P) are \( (x+5), 13 \) and \( (5 x-3) \). (a) value of \( x \) :
Ask by Ellis Lewis. in Gambia
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 4 \)
Solution
To find the value of \( x \) in the given Arithmetic Progression (A.P), let's analyze the information provided:
**Given:**
- First term: \( a_1 = x + 5 \)
- Second term: \( a_2 = 13 \)
- Third term: \( a_3 = 5x - 3 \)
**Property of A.P:**
In an A.P., the difference between consecutive terms is constant. Therefore,
\[
a_2 - a_1 = a_3 - a_2
\]
**Substitute the given terms:**
\[
13 - (x + 5) = (5x - 3) - 13
\]
**Simplify the equation:**
\[
13 - x - 5 = 5x - 16
\]
\[
8 - x = 5x - 16
\]
**Rearrange to solve for \( x \):**
\[
8 + 16 = 5x + x
\]
\[
24 = 6x
\]
\[
x = \frac{24}{6}
\]
\[
x = 4
\]
**Answer:**
\[
\boxed{4}
\]
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Simplify this solution Bonus Knowledge
Let's dive into the problem! In an Arithmetic Progression, the difference between consecutive terms is constant. Given the first three terms are \( (x+5) \), \( 13 \), and \( (5x-3) \), we can express this relationship mathematically: \[ 13 - (x + 5) = (5x - 3) - 13 \] Simplifying the left side: \[ 13 - x - 5 = 8 - x \] Now, simplifying the right side: \[ 5x - 3 - 13 = 5x - 16 \] Setting these two expressions equal gives us: \[ 8 - x = 5x - 16 \] Bringing all \( x \) terms to one side and constants to the other: \[ 8 + 16 = 5x + x \] Which simplifies to: \[ 24 = 6x \] Thus, solving for \( x \): \[ x = 4 \] So the value of \( x \) is \( 4 \). Now you’re ready to rock the next question!
