Question

find the value of x such that 7x+3, 8x+5, 3x-2 will form the A.P​

Answer 1

Answer:

7x+3,8x+5,3x-2

a2-a1= 8x+5-(7x+3)

8x+5-7x-3

x-2______(1)

a3-a2=3x-2-(8x+5)

3x-2-8x+5

-5x+3_____(2)

As these are in AP

So, common difference is also same that is -

a3-a2=a2-a1

from equation 1 and 2

-5x+3=x-2

-5x-x =-2-3

-6x=-5

x=5/6

Hope it helps you.

Answer 2

Answer:

Required value of x is (-1/6).

Step-by-step explanation:

Given series is 7x+3, 8x+5, 3x-2.

We know nth term of AP series,

$a_n = a + (n - 1)d$

Where, a is the first term of the series and d is common difference of term of the series.

Here,

$a = 7x + 3\\ d= (8x + 5) - (7x + 3) = x - 2$

According to question,

$a_3 = 7x + 3 + (3 - 1) \times (x - 2) \\ 3x - 2= 7x + 3 + 2x - 4\\ 3x - 7x - 2x=3 - 4 + 2 \\ - 6x = 1 \\ x = - \frac{1}{6}$

Therefore, required value of x is -1/6.

Some formulas of AP series are

$a_n=a_1+(n-1)d \\ S_n= \frac{n}{2} [2a+(n-1)d] \\ d=a_n -a_n-1 \\ S_n= \frac{n}{2} [a_1+a_n]$

Know more about Arithmetic progression

1) https://brainly.in/question/4219484

2) https://brainly.in/question/2768711

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