Question

A firm produces produces 1000 sets of TV during the 1st year. The total sets produced in 5 years is 7,000. Estimate the annual rate of increase in production, if the increase in each year is uniform

Answer 1

Answer:

The annual rate of increase in TV production is of $200 sets$.

Step-by-step explanation:

Given,

The production of $1st$ year of TV = $1000 sets$

The total set production in $5 years$ = $7000 sets$

The annual rate of increase in the TV production =?

The rate of increase each year is uniform.

Therefore, production in these years forms an AP ( Arithmetic progression ) with the data:

• The first term, a = $1000$
• The $n^{th}$ term, n = $5$
• The sum of the n terms of an AP, $S_{n}$ = $7000$

Now,

• The annual rate of increase in production can be calculated by using the formula of the sum of the n terms of an AP, i.e., $S_{n}$ , given below:
• $S_{n} = \frac{n}{2} [2a + (n-1)d]$

Here,

• $S_{n}$ = The sum of the n terms of an AP
• n = The $n^{th}$ term
• a = The first term
• d = The common difference, i.e., the rate of increase

After putting the given values in the equation, we get:

• $S_{n} = \frac{5}{2} [2\times 1000 + (5-1)d]$
• $7000 = \frac{5}{2} [2000 + (4)d]$
• $14000 = 10000 + 20d$
• $20d = 4000$
• $d = 200$

Hence, the annual rate of increase in TV production is = $200 sets$.