Question

30th term of 3,8,13,18

Answer 1

Answer:

The 30th term is 148. The change in y (3,8,13,18) is +5. Add 5 to find the number next in sequence; subtract 5 to find the number previous in sequence.

Step-by-step explanation:

Numbers in sequence 0-10: -2, 3, 8, 13, 18, 23, 28, 33, 38, 43, 48.

Numbers in sequence 11-20: 53, 58, 63, 68, 73, 78, 83, 88, 93, 98.

Numbers in sequence 21-30: 103, 108, 113, 118, 123, 128, 133, 138, 143, 148.

If you didn't notice the pattern, every +5 (POSITIVE +5), the number in sequence either ends in a 3 or an 8. The equation of the line would be y=5x+5 because the slope ($\frac{rise}{run}$) is $\frac{5}{1}$, or 5. Applying Δy/Δx ("change in y over change in x": the y-intercept is 5 because the change in y is ±5 (in this explicit case: +5), and the change in x is ±1 (in this explicit case: +1).

The simplest way to find the equation of the line here is utilizing $\frac{y2-y1}{x2-x1}$. You can use any two points (±) to find the slope, such as (1, 3) and (2,8) ₋ looking at the table I inserted below, you can pick any two points - for instance, 1 & 3 would be (1, 3), 2 & 8 would be (2, 8), 3 & 13 would be (3, 13), and 4 & 18 would be (4, 18). You would find the y-intercept by identifying the change in y, which I did in the paragraph above.

To find slope:

Formula to find the distance between two points: $\frac{y2-y1}{x2-x2}$

Chosen two points: Point 1 (x1,y1): (1,3) and Point 2 (x2, y2): (2,8)

Y2-Y1 will provide the change in y and the rise of the slope. X2-X1 will provide the change in x and the run in slope. $\frac{8-3}{2-1}$=$\frac{5}{1}$ (8-3=5 and 2-1=1). Therefore, the change in y and rise of the slope is 5, and the change in x and the run in slope is 1. $\frac{5}{1}$ simplifies to 5, so the slope is 5.

The change in y provides the y-intercept. The change in y is 5.

Identifying slope and the y-intercept

y=mx+b is the formula for slope and y-intercept, AKA slope-intercept form.

M is the slope of the line, and b is the y-intercept, or the change in y. The y-intercept of this line is the value of y at the point where the line crosses the y axis. The y before the sign of equality (=) will stay as y, and the x after m, or the slope, will stay as x. It means y-axis=(m)x-axis + (b).

Equation of the Line

Therefore, the equation of the line is y=5x+5. I inserted a graph below in which I graphed the equation of the line, as well as a table for the terms.