Question

In which of the following situations, does the list of numbers involved make as arithmetic progression and why? (i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre. (iv)The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.

Answer 1

In situation i, iii, and iv list of numbers involved make as arithmetic progression.
As in situation <i> the first term is 15 and common difference is 8 thus AP is 15, 23, 31, 39....n. Similarly in <iii> and <iv> are also APs.