Math, asked by jeanburleigh5, 5 months ago

Ms. Clark earned $29,600 in her third year as a banker and $32,600 in her seventh year. How much did she make in her tenth year? Assume that her yearly salaries form an arithmetic sequence.
$28,100
$34,850
$55,550
$58,100

Answers

Answered by Anonymous
4

Answer:Assume it's an arithmetic sequence. a stands for the first salary, d stands for difference of each year, n stands the number of year

General formula for arithmetic sequence is

an = a + (n - 1)d

Given

a₃ = a + (3 - 1)d = 29,600

a₇ = a + (7 - 1)d = 32,600

Work on it:

First, with elimination, find the value of d

a + 2d = 29,600

a + 6d = 32,600

--------------------- - (substract)

     -4d = -3,000

        d = 750

The difference of each year is $750

Second, find the value of a with subtitution

a + 2d = 29,600

a + 2(750) = 29,600

a + 1,500 = 29,600

a = 29,600 - 1,500

a = 28,100

The salary on first year is $28,100

Third, find the salary in tenth year

an = a + (n-1)d

a₁₀ = a + (10 - 1)d

a₁₀ = 28,100 + 9(750)

a₁₀ = 28,100 + 6,750

a₁₀ = 34,850

Her salary in tenth year is $34,850. The answer is b

Step-by-step explanation:

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