Find the values of r1 and d for an arithmetic sequence r6 = 4 and r8= 5

  a. r1 = 3/2; d = 1/2

Step-by-step explanation:

You can use your number sense to solve this.

Terms r6 and r8 are two terms apart, so their difference will be 2 times the common difference:

  d = (r8 -r6)/2 = (5 -4)/2 = 1/2 . . . . . matches choices A and D

The given terms are even terms. Odd terms will be 'something and 1/2'. The first term of the sequence (n=1) is an odd term, so cannot be 1 (choice D). The only viable answer choice is A.

If you want to solve for r1, use the equation for the general term and put in the numbers for either r6 or r8. (We'll use r6.)

  rn = r1 +d(n -1)

  r6 = r1 +(1/2)(6 -1) = 4

  r1 = 4 -5/2 = 3/2 . . . . matches choice A

answer: standard form is ax^2 + bx + c = 0

step-by-step explanation:

standard form is ax^2 + bx + c = 0

(2x + 1)(x - 2) = 0

distribute to get into standard form

2x^2 - 4x + x - 2 = 0

2x^2 - 3x - 2 = 0

a = 2, b= -3, c = -2

a is your answer

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