Question

20. 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?

Answer 1

The longer side of trapezoid shaped garden is containing 97 and each row must be decreased by 2 on each end and the construction must stop when it reaches the 25th row.
here piont should notable that , 2 bricks are decreased on each ends . Means there are 4 bricks on each row.
Hence, sequence are 97, 93 , 89, 85 , 81 ........
25th term in this series ,
T₂₅ = 97 + (25 - 1)(-4)
= 97 - 96 = 1

Hence, total number of bricks = sum of 25 terms of given series
= 25/2 [ first term + last term ]
= 25/2 [ 97 + 1]
= 25 × 98/2
= 25 × 49
= 1225

Hence, number of bricks does he need to buy = 1225

Answer 2

General term or nth term of A.P
The general term or nth term of A.P is given by an or tn = a + (n – 1)d, where a = a1 is the first term, d is the common difference and n is the number of term.

Sum of n terms of an AP
The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by
Sn = n /2 [ 2a + ( n - 1) d] or
Sn=n /2 [ a + l ] (l = last term)

GIVEN :
Each row must be decreased by 2 on each end and the construction must stop when it reaches the 25th row. It means 4 bricks will decrease.

Then, the number of bricks in each row as a sequence 97,93,89,............
Here,a=97, d = 93-97 = -4 , n = 25

Sn = (n/2) [2a+(n-1)d]
S25 = (25/2) [2(97) + (25-1) (-4)]
S25 = (25/2) [194 + (24) (-4)]
S25 = (25/2) [194 - 96]
S25= (25/2) (98)
S25= 25 x 49
S25= 1225 bricks

Hence, he needs to buy 1225 bricks.

HOPE THIS WILL HELP YOU...