ind an equation for the nth term of the arithmetic sequence.a14 = -33, a15 = 9

Accepted Solution

Answer:[tex]a_n=42n-621[/tex]Step-by-step explanation:This is arithmetic sequence so you should go to linear equations in your head.Think of the question asking you to find the equation of line going through the points:(14,-33) and (15,9).First, let's find the slope.You need to compute y's change over x's change.The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.Like this: (  15  ,   9)-(  14  ,  -33)------------------    1         42So the slope is 42/1=42.(The slope is our common difference.)Now point slope form is:y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.So we have m=42 and (x1,y1)=(15,9).  (You could have chose the other point.)y-9=42(x-15)I'm going to put in slope-intercept form.  Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.y-9=42(x-15)Solve for y by adding 9 on both sides:y=42(x-15)+9Distribute 42 to terms in the ( ) :y=42x-42(15)+9y=42x-630+9y=42x-621So we can which back to n now:[tex]a_n=42n-621[/tex]