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5. The first 6 terms of an arithmetic sequence are plotted on a grid. The coordinates of two points on the graph are (3,11) and (6,23). What is the expression for the general term of the sequence?​

Sagot :

Answer:

An = 6n - 7

Step-by-step explanation:

Given: (3,11) and (6,23)

The formula of Arithmetic sequence

  • An = A1+(n-1)d

For (3,11)

  • A(3) = A1 + (3-1)d
  • 11 = A1 + 2d

For (6,23)

  • A(6) = A1 + (6-1)d
  • 23 = A1 + 5d

Subtract the two solved equations:

23 = A1+5d

- 11 = A1 + 2d

------------------------------

= 12 = +2d

12/2 = d

6 = d

Now , we solve for the A1 by substituting the values

  • An = A1 + (n-1)d
  • A(3) = A1 + (3-1)6
  • 11 = A1 + 2(6)
  • 11 = A1 + 12
  • 11 - 12 = A1
  • - 1 = A1

Again , we know that

  • An = A1+(n-1)d

We therefore substitute the value of d and A1 to get the general rule

  • An = -1 + (n-1)6
  • An = -1 + 6n-6
  • An = 6n - 7