Question

Hello, Can you help me with the following question:My family is planning to build a brick wall that approximates the shape of a trapezoid. The shorter base of the trapezoid needs to start with a row of 5 bricks, and each row must increase by 2 bricks on each side until there are 20 rows. How can I go about finding out how many bricks I will need to buy so that I don’t spend more money than needed?

Answer 1

In this problem, we have the sequence

5,9,13,17,21,...

Is an arithmetic sequence

the common difference is d=4

there are 20 terms (rows) in the sequence

Remember that

The rule to find the sum of the first n terms of the arithmetic sequence is equal to

`S=(n)/(2) [2a_1+(n-1)d]`

where

n=20

a1=5 ----> first term

d=4

substitute given values

`S=(20)/(2)[2(5)+(20-1)4]`

S=860

therefore

The answer is 860 bricks