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statuscvo [17]
3 years ago
7

Find a formula for a_n (for the geometric sequence), then find the 8th term. Solve for both or one of these questions, thank you

so much!

Mathematics
1 answer:
kati45 [8]3 years ago
4 0

Answer:

2a. aₙ = 12 * -2ⁿ⁻¹; a₈ = -1536

2b. aₙ = 4 * 3ⁿ⁻¹; a₈ = 8748

Step-by-step explanation:

The geometric sequence formula is aₙ = a₁ * rⁿ⁻¹.

2a:

a₈ = 12 * -2⁸⁻¹ <em>{Subtract 1 from 8 to get 7}</em>

a₈ = 12 * -2⁷ <em>{2⁷ is 128. Since the exponent is odd, this will be negative.}</em>

a₈ = 12 * (-128) <em>{Multiply 12 by -128 to get -1536.</em>

a₈ = -1536

2b:

a₈ = 4 * 3⁸⁻¹ <em>{Subtract 1 from 8 to get 7)</em>

a₈ = 4 * 3⁷ <em>{7 is the 3rd number after 4 (a multiple of 4). As a result, this will end in a 7. 3⁷ is 218</em><em>7</em><em>.}</em>

a₈ = 4 * 2187 <em>{Multiply 4 by 2187 to get 8748}</em>

a₈ = 8748

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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
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Step-by-step explanation:

<u>Step 1: Define Equation</u>

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<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 2x on both sides:                    3 = 0.5x
  2. Divide 0.5 on both sides:               6 = x
  3. Rewrite:                                           x = 6

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in<em> x</em>:                    3 - 2(6) = -1.5(6)
  2. Multiply:                               3 - 12 = -9
  3. Subtract:                              -9 = -9

Here we see that -9 does indeed equal -9.

∴ x = 6 is the solution to the equation.

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