The terms \( x \), \( 0.5x + 7 \), and \( 3x - 1 \) are consecutive terms of an arithmetic sequence.

How do I determine the value of \( x \) and state the three terms?

So you know that for arithmetic sequences, the difference between each term is the same. So we can use this to form an equation:
Difference between term 2 and 1 = Difference between term 3 and 2
( 0.5 x + 7 ) − x = ( 3 x − 1 ) − ( 0.5 x + 7 ) − 0.5 x + 7 = 2.5 x − 8 15 = 3 x x = 5
So the three values are: ** **5, 0.5(5)+7, 3(5)-1
= 5, 9.5, 14

Answered by ollieboyne | 2024-06-10

To find the value of x for the arithmetic sequence terms, set up an equation based on the constant difference between terms, which yields x = 5. The sequence terms are 5, 9.5, and 14.
The question involves finding the value of x when x, 0.5x + 7, and 3x - 1 are consecutive terms of an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant. To find x, we set up an equation where the difference between the second and first term is equal to the difference between the third and second term.
0.5x + 7 - x = 3x - 1 - (0.5x + 7)
-0.5x + 7 = 2.5x - 8
3x = 15
x = 5
Now we plug this value into the terms of the sequence:

First term: x = 5
Second term: 0.5(5) + 7 = 9.5
Third term: 3(5) - 1 = 14

The terms of the sequence are 5, 9.5, and 14.

Answered by HenryCharles | 2024-06-24

To find the value of x for the terms in the arithmetic sequence, we equated the differences between the terms and solved for x , which gave x = 5 . The three terms of the sequence are 5 , 9.5 , and 14 .
;

Answered by ollieboyne | 2024-12-26