Question

please help me with this question.​

Answer 1

Step-by-step explanation:

It is given that the longer side of trapezoid needs to start with a row of 97 bricks and each row must be decreased by 2 on each end and the construction should stop at 25th row.

Let us write the number of bricks in each row as an arithmetic sequence as follows:

97,93,89,

Now, we need to find the number of bricks needed to buy and for that we have to write the above sequence as series that is

97+93+89+

The first term of the series is a

1

=97, the second term is a

2

=93 and so on.

We find the common difference d by subtracting the first term from the second term as shown below:

d=a

2

−a

1

=93−97=−4

We know that the sum of an arithmetic series with first term a and common difference d is S

n

=

2

n

[2a+(n−1)d]

Thus, substitute a=97,d=−4 and n=25 in S

n

=

2

n

[2a+(n−1)d] as follows:

S

25

=

2

25

[(2×97)+(25−1)(−4)]=

2

25

[194+(24×−4)]=

2

25

[194−96]=

2

25

×98=25×49=1225

Hence, the gardener needs to buy 1225 bricks.