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

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 = (n)/(2) \Bigg(2a + (n-1) d\Bigg)}}}`

By substituting values :

`\tt : \implies S_n = (14)/(2) \Bigg(2(1700000) + (14-1) (4000)\Bigg)`

`\tt : \implies S_n = \cancel{(14)/(2)} \Bigg(2* 1700000 + 13 * 4000\Bigg)`

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

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

`\tt : \implies S_n = 7 * 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.

Answer 2

9514 1404 393

Answer:

$24,164,000

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.