find the value of x if the arithmetic mean of 3 and 3x + 5 is a determine the arithmetic sequence and the common difference
Answers
Therefore the value of x is 8/3.
Step-by-step explanation:
The arithmetic mean for 3 and 3x + 5 is 8, that is
Given:
1st term 2nd term 3rd term
3, 8, 3x + 5
Number of terms n = 3
Common difference d = 8
To get the common difference, subtract
common difference d = 2nd term - 1st term
d = 8 - 3
d = 5
common difference d = 3rd term - 2nd term
d = 3x + 5 - 8 Subtract 5 - 8
d = 3x - 3
Equate both computed comon difference
5 = 3x - 3 Transpose -3 to the left side of the equation
5 + 3 = 3x Simplify
8 = 3x Divide 3 to both sides of the equations
3 3
8/3 = x
Therefore the value of x in the question is 8/3.
To check, substitute the value of x to the third term which is 3x + 5
=3x + 5
=3(8/3) + 5
=8 + 5
= 13
1st term 2nd term 3rd term
3 8 13
Making the above sequence arithmetic with a common difference of 5
To learn more about arithmetic means, please click the links below;
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