Question

A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly be a fixed number every year, find

(i) the production in the first year

(ii) the total product in 7 years and

(iii) the product in the 10^th year.

Answer 1

Let the number of Radio manufactured increase by x each year be a. So, A.P. formed ATQ is

a, a + x, a + 2x, ....

Here,

$a_3=a+2x=600\dots \dots \left(i\right)$

$a_7=a+6x=700\dots \dots \left(ii\right)$

From (i) and (ii)

a = 550, x = 25

(i) 550 Radio's were manufactured in the first year.

(ii) The total produce in 7 years is sum of produce in the first 7 years.

$S_7=\frac{7}{2}[550+700][\because S_n=\frac{n}{2}[a+l\left]\right]$

= 4375

4375 Radio's were manufactured in first 7 years.

(iii) The produce in 10th year

$a_{10}=a+9d$

= 550 + 9(25) = 775

775 Radio's were manufactured in the 10th year.