Question

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.

Answer 1

She gets an increase of $750 each year so in the tenth year she would make $34,850

Answer 2

Ms. Clark will make $ 34,850 in her tenth year.

What is an arithmetic progression?

An arithmetic progression, also known as an arithmetic sequence, is a set of numbers in which the difference between successive terms remains constant.

$a_{n}$ = a + (n-1)d

Let the amount she made in her 1st year = a

The increment she gets each year = d

$a_{3}$ = a + 2d

29600 = a + 2d ..(1)

$a_{7}$ = 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

$a_{10}$ = a + 9d

$a_{10}$ = 28100 + 9 ( 750 )

$a_{10}$ = $34850

Hence, Ms. Clark will make $ 34,850 in her tenth year.

Learn more about progressions on:

https://brainly.com/question/13989292

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