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
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: