A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of $97$ bricks. Each row must be decreased by $2$ bricks on each end and the construction should stop at $25 t h$ row. How many bricks does he need to buy?

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Solution

The longer side of trapezoid shaped garden is containing $97$ bricks and each row must be decreased by $2$ on each end and the construction must stop when it reaches the $25 t h$ row.

If we write the number of bricks in each row as sequence we will get $97, 93, 89, . . . . . . . . . . . .$
Now we need to find number of bricks needed to buy. For that we have to make it as series and we have to find for $25 t e r m s$ of the series.
$S_{n} = (\frac{n}{2}) [2 a + (n - 1) d]$
Here, $a = 97, n = 25$ and $d = 93 - 97 = - 4$
$S_{25} = (\frac{25}{2}) [2 (97) + (25 - 1) (- 4)]$
$= (\frac{25}{2}) [194 + (24) (- 4)]$
$= (\frac{25}{2}) [194 - 96]$
$= (\frac{25}{2}) (98)$
$= 25 \times 49$
$= 1225$ bricks

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A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of 97 bricks. Each row must be decreased by 2 bricks on each end and the construction should stop at 25th row. How many bricks does he need to buy?

A gardener plans to construct a trapezoidal shaped structure in his garden. The longer side of trapezoid needs to start with a row of $97$ bricks. Each row must be decreased by $2$ bricks on each end and the construction should stop at $25 t h$ row. How many bricks does he need to buy?