Michelle is a marine biologist. She accepted a job that pays $46 850 in the first year and $56 650 in the eighth year. Her salary is an arithmetic sequence with eight terms.
a) In what year will her salary first exceed $50 000?
Answers
Given : A job pays $46 850 in the first year and $56 650 in the eighth year.
Salary is an arithmetic sequence with eight terms.
To Find : In what year will her salary first exceed $50 000?
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
a = 46850
n = 8
a₈ = 56650
a₈ = a + (8-1)d
=> 56650 = 46850 + 7d
=> 9800 = 7d
=> d = 1400
in nth year salary first exceed $50000
=> a + (n - 1)d >50000
=> 46850 + (n - 1)1400 > 50000
=> (n - 1)1400 > 3150
=> (n - 1) > 2.25
=> n > 3.25
Hence n = 4
so in 4th Year , salary first exceed $50000
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