![Identify the given information:
Sn = Php 1,000,000.00(amount to be
distributed)
n= 5 (number of child)
d = -50,000.00
Solution:
Using the formula:
Sn =
𝑛
2
[ 2A1 + (n – 1)d ]
1,000,000 =
5
2
[ 2A1 + (5 – 1)-50,000]
2,000,000 = 5[ 2A1 + (4)-50,000 ]
2,000,000 = 5[2A1 – 200,000]
2,000,000 = 10A1 – 1,000,000
2,000,000 + 1,000,000 = 10A1
3,000,000 = 10A1
3,000,000
10
= A1
300,000 = A1
A1 = 300,000
A2 = A1 – 50,000 = 250,000
A3 = A2 -50,000 = 200, 000
A4 = A3 – 50,000 = 150,000
A5 = A4 – 50,000 = 100,000
Therefore, each child receives the amount
in the sequence of Php300,000,
Php250,000, Php200,000, Php150,000,
Php100,000](https://image.slidesharecdn.com/activitysequenceandseries-201023024735/85/Activity-sequence-and-series-3-320.jpg)
![Identify the given information.
An = 15 boxes (last term)
A1 = 1 (first box of 1st element)
d = 1 (common difference)
n= (15 number of rows)
Sn = ?
Solution:
Using the formula:
Sn =
𝒏
𝟐
[ 2A1 + (n – 1)d ]
Sn =
15
2
[ 2(1) + (15 – 1)1 ]
Sn =
15
2
[ 2 + (14)1 ]
Sn =
15
2
[2 + 14]
Sn =
15
2
[16]
Sn = 120
Or using the formula
Sn =
𝒏
𝟐
( A1 + An)
Sn =
15
2
( 1 + 15)
Sn =
15
2
(16)
Sn = 120
The number of boxes of detergent are needed
for the pyramid is 120.](https://image.slidesharecdn.com/activitysequenceandseries-201023024735/85/Activity-sequence-and-series-5-320.jpg)
![Identify the given information:
d = 2 (common difference)
An= 26
n = 13 = (
26
2
) = since there are 2
fewer blocks in each successive row
thereafter.
A1 = 2
Solution:
Using the formula:
Sn =
𝒏
𝟐
[ 2A1 + (n – 1)d ]
Sn =
13
2
[ 2(2) + (13 – 1)2 ]
Sn =
13
2
[ 4 + (12)2 ]
Sn =
13
2
[ 4 + (24 ]
Sn =
13
2
[ 28 ]
Sn = 182
Or use the formula Sn =
𝑛
2
( A1 + An)
Sn =
13
2
( 2 + 26)
Sn =
13
2
[ 28 ] = Sn = 182
There are 182 blocks in the
pyramid.](https://image.slidesharecdn.com/activitysequenceandseries-201023024735/85/Activity-sequence-and-series-7-320.jpg)
Activity sequence and series
- 2. Problem Solving 1. The amount of Php 1,000,000.00 is distributed among five people so that each person after the first receives Php 50,000.00 less than the preceding person. How much does each child receive?
- 3. Identify the given information: Sn = Php 1,000,000.00(amount to be distributed) n= 5 (number of child) d = -50,000.00 Solution: Using the formula: Sn = 𝑛 2 [ 2A1 + (n – 1)d ] 1,000,000 = 5 2 [ 2A1 + (5 – 1)-50,000] 2,000,000 = 5[ 2A1 + (4)-50,000 ] 2,000,000 = 5[2A1 – 200,000] 2,000,000 = 10A1 – 1,000,000 2,000,000 + 1,000,000 = 10A1 3,000,000 = 10A1 3,000,000 10 = A1 300,000 = A1 A1 = 300,000 A2 = A1 – 50,000 = 250,000 A3 = A2 -50,000 = 200, 000 A4 = A3 – 50,000 = 150,000 A5 = A4 – 50,000 = 100,000 Therefore, each child receives the amount in the sequence of Php300,000, Php250,000, Php200,000, Php150,000, Php100,000
- 4. Problem Solving 2. In a display window, a store owner planned to place boxes of detergent in pyramid form so that the bottom row contains 15 b0xes, and so on, with one box on top. How many boxes of detergent are necessary for the pyramid?
- 5. Identify the given information. An = 15 boxes (last term) A1 = 1 (first box of 1st element) d = 1 (common difference) n= (15 number of rows) Sn = ? Solution: Using the formula: Sn = 𝒏 𝟐 [ 2A1 + (n – 1)d ] Sn = 15 2 [ 2(1) + (15 – 1)1 ] Sn = 15 2 [ 2 + (14)1 ] Sn = 15 2 [2 + 14] Sn = 15 2 [16] Sn = 120 Or using the formula Sn = 𝒏 𝟐 ( A1 + An) Sn = 15 2 ( 1 + 15) Sn = 15 2 (16) Sn = 120 The number of boxes of detergent are needed for the pyramid is 120.
- 6. Problem Solving 3. A pyramid of blocks has 26 blocks in the bottom row and 2 fewer blocks in each successive row thereafter. How many blocks are there in the pyramid?
- 7. Identify the given information: d = 2 (common difference) An= 26 n = 13 = ( 26 2 ) = since there are 2 fewer blocks in each successive row thereafter. A1 = 2 Solution: Using the formula: Sn = 𝒏 𝟐 [ 2A1 + (n – 1)d ] Sn = 13 2 [ 2(2) + (13 – 1)2 ] Sn = 13 2 [ 4 + (12)2 ] Sn = 13 2 [ 4 + (24 ] Sn = 13 2 [ 28 ] Sn = 182 Or use the formula Sn = 𝑛 2 ( A1 + An) Sn = 13 2 ( 2 + 26) Sn = 13 2 [ 28 ] = Sn = 182 There are 182 blocks in the pyramid.