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shtirl [24]
3 years ago
12

The fourth term in an arithmetic sequence is 18 and the seventh term is 39. If the first term is a1 , which is an equation for t

he nth term of this sequence?
Mathematics
1 answer:
evablogger [386]3 years ago
8 0

Answer:

<h2>            aₙ = 7n - 10</h2>

Step-by-step explanation:

The nth term:  a_n=a_1+d(n-1)

So:

    a₄ = a₁ + 3d

18 =  a₁ + 3d   ⇒   3d =  18 - a₁

    a₇ = a₁ + 6d

39 = a₁ + 6d

39 = a₁ + 2(18 - a₁)

39 = a₁ + 36 - 2a₁

39 = 36 - a₁

a₁ = -3

3d = 18 - (-3)

3d = 21

d = 7

So the nth term:

                            a_n = -3 + 7(n-1)\\\\a_n=-3 +7n - 7\\\\a_n = 7n - 10

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
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  4. Multiplication
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  1. Substitute in points [Slope Formula]:                                                          \displaystyle m=\frac{-5-1}{0--2}
  2. [Fraction - Denominator] Simplify:                                                                \displaystyle m=\frac{-5-1}{0+2}
  3. [Fraction - Numerator] Subtract:                                                                     \displaystyle m=\frac{-6}{0+2}
  4. [Fraction - Denominator] Add:                                                                      \displaystyle m=\frac{-6}{2}
  5. [Fraction] Divide:                                                                                             \displaystyle m=-3
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