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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.
a. $28,100
b. $34,850
c. $55,100
d. $58,100

Respuesta :

jongdae21
Answer is B. 34,850.

Using formula Un = a+(n-1)d

For third year,
29600 = a + 2d
For seventh year,
32600 = a + 6d

solve the simultaneous equations to find for a, and d, and substitute into U10 = a + 9d (from formula.) a should be 28100, and d should be 750.
gustanika
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

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