Question

Rylee earns $5,4000 in her first year of teaching and earns a 3% increase in each successive year. Write a geometric series formula SN for Rylee's total earning over and years. Use this formula to find Rylee's total earnings for first 20 years of teaching to the nearest cent.

Answer 1

Answer: $1387800

Step-by-step explanation:

This is an sum of Arithmetic Progression with the formula

Sum of nth term

Sn = n/2( a + l ) --------------- 1

where l = a + ( n - 1 )d -------2

Now put (2) in 1

Sn = n/2{( a + a + (n - 1)d}

= n/2{( 2a + ( n -1 )d}

From the question

a = $5,4000 ( firs term )

d = 3% of $5,4000 ( common difference ), n = 20 years. Solution to question one therefore is.

First find 3% of $54000 = $1620, so the geometric series is

Sn = n/2{(2a + ( n - 1 )d

Second solution is substitution,

Sn. = 20/2 {(2 x 54000 + (20 -1)1620)}

= 10{ 108000 + 19 x 1620}

= 10{ 108000 + 30780 }

= 10{ 138780 }

= 1387800

Therefore, the total emoluments of Rylee for the past 20 years

= $1387800