Question

The first three terms of an ap respectively are 5x-1 , 5x + 7 and 7x+1.then value of x is ​

Answer 1

Question :-

The first three terms of an AP respectively are 5x -1 , 5x +7 and 7x +1

then find the value of x -

Answer :-

→ x = 7

To find :-

→ Value of x.

Explanation :-

Given that ,

• First term = 5x -1

• second term = 5x +7

• third term = 7x + 1

we know that ,

→ The average of first and third term of an AP is equal to the second term of that AP ( Arithmetic progression)

$\sf \frac{first \: term + third \: term}{2} = second \: term \\ \\ \rightarrow \sf \frac{5x - 1 + 7x + 1}{2} = 5x + 7 \\ \\ \rightarrow \sf\frac{12x}{2} = 5x + 7 \\ \\ \rightarrow \sf{ 12x = 10x + 14} \\ \\ \rightarrow \sf12x - 10x = 14 \\ \\ \rightarrow \sf 2x = 14 \\ \\ \rightarrow \boxed{\sf \: x = 7}$

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hope it will help you.