powerpoint presentation

1. ACTIVITY 2:
Arithmetic Sequence
and Series

2. Problem no. 1
The amount of Php 3, 000, 000 is distributed among
four people so that each person after the first
receives Php 150, 000.00 less than the preceding
person. How much does each child receive?

3. Solution:
Sn = 3,000,000
d = -150,000
n = 4
Sn =
𝑛
2
[ 2(A1 + (n- 1)d ]
3,000, 000 =
4
2
[ 2(A1) + (4- 1) -150,000 ]
3,000,000 = 2 [ 2A1 + (5)-150,000 ]
3,000,000 = 2 [ 2A1 - 450,000 ]
3,000,000 = [ 4A1 - 900,000 ]
3,000,000 + 900,000 = 4A1
3,900,000 = 4A1
975,000 = A1
A1 = 975,000
A2 =A1 – 150,000 = 825,000
A3 = A2 – 150,000 = 675,000
A4 = A3 – 150,000 = 525,000

4. Problem no. 2
• Anna’s grade on the first of twelve quizzes in her
algebra course was 45. Howerver, on each
succeeding quiz, her score was five more than the
preceding one. What was the arithmetic mean
(average score) of the twelve scores?

5. Solution :
A1 = 45
d = 5
n = 12
An = A1 + (n – 1)d
A12 = 45 + (12 – 1)5
A12 = 45 + (11)5
A12 = 45 + 55
A12 = 100
Since the last term is 100 or the 12th
term we can compute the average
score.
Sn =
𝑛
2
(A1 + An)
Sn = 12 (45 + 100)
Sn = 12 (145)
Sn = 870
Average score =
870
12
= 72. 5
So, the average score of twelve
quizzes is 72. 5

6. Problem 3.
• The balcony of a theatre has 12 rows. Of seats. The
last row contains 8 seats, and each of the other
rows contains one more seat than the row behind
it. How may seats are there in the balcony?

7. Solution:
n = 12
A1 = 8
d = 1
An = A1 + (n – 1)d
A12 = 8 + (12 – 1)1
A12 = 8 + (11)1
A12 = 8 + 11
A12 = 19
Sn =
𝑛
2
( A1 + An)
Sn =
12
2
(8 + 19)
Sn = 6 (27)
Sn = 162
There are 162 seats in the
balcony.