(11) A TV manufacturer has produced 1000 TVs in the seventh year and 1450 TVs in the tenth year. Assuming that the production increases uniformly by a fixed number every year, find the number of TVs produced in the first year, find the number of TVs produced in the first year and 15th year.

Solution:

Number of TVs produced in the seventh year = 1000

Number of TVs produced in the tenth year = 1450

        t7 = 1000

        t10 = 1450

a + 6 d = 1000   ----- (1)

a + 9 d = 1450   ----- (2)

(1) – (2)

 Subtracting second equation from first equation

                                a + 6 d = 1000

                                a + 9 d = 1450

                        (-) (-) (-)

                      ------------------

                        -3d = -450

                          d = -450/(-3)

d = 150

Substitute d = 150 in the first equation

                   a + 6(150) = 1000

                   a + 900 = 1000

                          a = 1000 -900

                          a = 100

Therefore number of TVs produced on the first year is 100

To find number of TVs produced in the 15th year year we have to find the 15th term of the A.P

tn = a + (n-1) d

t15 = 100 + (15-1) 150

t15 = 100 + 14(150)

     = 100 + 2100

     = 2200