Question

The salary scale for an officer starts at $1,700,000 .A rise of $4000 is given at the end of each share . Find the total amount of money the officer will earn in 14 years

Answer 1

9514 1404 393

Answer:

  $24,164,000

Step-by-step explanation:

The yearly salaries form an arithmetic sequence with a first term of 1700000 and a common difference of 4000.

The sum of n terms of an arithmetic sequence with first term a1 and common difference d is ...

  Sn = (2a1 +d(n -1))(n/2)

For the given numbers, the sum of 14 years' salaries will be ...

  S14 = (2·1,700,000 +4,000(14 -1))(14/2) = 24,164,000

The officer will earn $24,164,000 in a 14-year period.

Answer 2

Given :

• Salary at starting = $ 1,700,000
• Rise in salary at the end of each share = $ 4000
• No. of years = 14

To Find :

• The total amount of money the officer will earn in 14 years = ?

Solution :

Clearly, we can see that salary of the officer is in form of Arithmetic progession, where :

• First term, a = $ 1,700,000
• Common difference = $ 4000
• Number of terms, n = 14

And we have to find total salary i.e. $\tt s_{n} = ?$

Now, we know that :

$\large \underline{\boxed{\bf{S_n = \dfrac{n}{2} \Bigg(2a + (n-1) d\Bigg)}}}$

By substituting values :

$\tt : \implies S_n = \dfrac{14}{2} \Bigg(2(1700000) + (14-1) (4000)\Bigg)$

$\tt : \implies S_n = \cancel{\dfrac{14}{2}} \Bigg(2\times 1700000 + 13 \times 4000\Bigg)$

$\tt : \implies S_n = 7 \Bigg(3400000 + 52000\Bigg)$

$\tt : \implies S_n = 7 \Bigg(3452000\Bigg)$

$\tt : \implies S_n = 7 \times 3452000$

$\tt : \implies S_n = 24164000$

$\large \underline{\boxed{\bf{S_n = \ 24,164,000}}}$

Hence, the total amount of money the officer will earn in 14 years is $ 24,164,000.