# Arithmetic Sequence Word Problem

. Lucy Ango’yuaq, from Baker Lake, Nunavut, is a prominent wall hanging artist. This wall hanging is called Geese and Ulus. It is 22 inches wide and 27 inches long and was completed in 27 days. Suppose on the first day she completed 48 square inches of the wall hanging, and in the subsequent days the sequence of cumulative areas completed by the end of each day produces an arithmetic sequence. How much of the wall hanging did Lucy complete on each subsequent day? Express your answer in square inches.

length of painting =27 inches

breath of painting = 22 inches

This shows that wall hanging is in a rectangular shape which is apparent from the diagram as well. Therefore area of hanging = length * breath = 27*22=594 sq inches.

Hanging completed on first day = 48 inches, since after first day she completed the Hanging in an arithmetic sequence on subsequent days.

Therefore area of painting left to complete after first day =594-48=546 sq inches,

Than also, days left= total days-first day = 27-1 =26 days.

So hanging completed by Lucy each day = total area of hanging reaming to complete÷days left

                                 = 546 ÷ 26 = 21 sq inches a day