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.
She gets an increase of $750 each year so in the tenth year she would make $34,850
Ms. Clark will make $ 34,850 in her tenth year.
An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant.
@@MATH_TOKEN_0@@ = a + (n-1)d
Let the amount she made in her 1st year = a
The increment she gets each year = d
@@MATH_TOKEN_1@@ = a + 2d
29600 = a + 2d ..(1)
@@MATH_TOKEN_2@@ = a + 6d
32600 = a + 6d ..(2)
Subtract the 1st equation from the 2nd equation:
4d = 3000
d = $750
Put the value of d in 1st equation:
a = $28100
@@MATH_TOKEN_3@@ = a + 9d
@@MATH_TOKEN_4@@ = 28100 + 9 ( 750 )
@@MATH_TOKEN_5@@ = $34850
Hence, Ms. Clark will make $ 34,850 in her tenth year.
Learn more about progressions on:
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