Question

A firm manufactured 1000 Tv sets during its first year.the total firms production during the 10 year of operationis 29035 sets .

For each the level of output for 15th year using per year constant increase in production .

Answer 1

6922 TV sets

Explanation:

You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.

Arithmetic series

An arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...

an = a1 +d(n -1)

And the sum of n terms is ...

Sn = (2a1 +d(n-1))(n/2)

Application

To find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.

S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000

29035 = 10000 +45d . . . . . . . . . . . simplified

d = (29035 -10000)/45 = 423 . . . . the increase in production each year

Production in the 15th year is ...

a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922

The output in the 15th year was 6922 TV sets.