Grade 10 week 7 Mathematics Geometric Series

1. CHOOSE THE BOX THAT YOU WANT!!!

2. What is the Formula for
Geometric sequence?

3. What is the formula to find
the ratio?

4. What is the Formula to find the
arithmetic sequences ?

5. What is the formula for the
sum of the arithmetic
sequence?

6. What is the Formula for Geometric
sequence?
𝑎𝑛 = 𝑎1 𝑟𝑛−1

7. What is the formula to find the
ratio?
𝑎4
𝑎3
=
𝑎3
𝑎2

8. What is the formula for the
sum of the arithmetic
sequence?
𝑆𝑛 =
𝑛
2
(𝑎1 + 𝑎𝑛)

9. What is the Formula to find the
arithmetic sequences ?
𝑎𝑛 = 𝑎1 + ( n – 1 ) d

10. “ The effectiveness of work increases
according to geometric progression if
there are no interruptions.”
~Andre Maurois

11. What is the math topic today?

12. Geometric Series
Presented By: Romeo Prado Norbe Jr.

13. A geometric series is the indicated sum of the
terms of a geometric sequence. The formula for
the partial sum , 𝑆𝑛 of a geometric series are
𝑆𝑛 =
𝑎1(1−𝑟𝑛)
1−𝑟
, r ≠ 1 and 𝑆𝑛 =
𝑎1−𝑟𝑡𝑛
1−𝑟
Geometric Series

14. Where n is the number of terms, 𝑎1 is the
first term, r is the common ratio, and 𝑎𝑛 is the
last term

15. Example 1: Find the sum of the eleven terms of the geometric
series -5, -10, -20
Solution:
r =
−10
−5
=
−20
−10
= 2 Find the common ratio.
𝑆𝑛 =
𝑎1(1−𝑟𝑛)
1−𝑟
Use the formula.
𝑆11 =
−𝟓 (1−211)
1−2
Substitute n = 11 𝑎1= -5, r = 2
𝑆11 = −10,235
The sum of the first eleven
terms is −10,235.

16. Example 2: In geometric series 𝑎1= 2, 𝑎7 = 1,458, r = 3. Find 𝑆7.
Solution:
𝑆𝑛 =
𝑎1 − 𝑟𝑡𝑛
1 − 𝑟
Use the formula.
𝑆7 =
2−3(1,458)
1−3
Substitute 𝑎1= 2 𝑡7= 1,458, r=3.
𝑆7 = 2,186
The sum of the first seven terms
is 2,186.

17. Example 3: How many terms of geometric progression 2, 6, 18,…
must be taken so that their sum is 6,560?
Solution:
6,560 =
2(1−3𝑛)
1−3
Substitute 𝑆𝑛= 6,560 𝑡1= 2, r=3.
-13,120 = 2 − 2(3𝑛)
6,561 =3𝑛
38
= 3𝑛
8 = n
Solve for the n.
The number of term is 8.

18. Example 4: A cell divides into two every 50 seconds. There are
10 cells at the start of the experiment. How many cells will be there
be at the end of 5 minutes
Solution:
n=
5(60)
50
= 6
r =
20
10
= 2
Find n, the number of times the
cells will divide after 5
minutes. Find r.
𝑆𝑛 =
𝑎1(1−𝑟𝑛)
1−𝑟
Use the formula.
𝑆6 =
𝟏𝒐 (1−26)
1−2
Substitute n = 6, r = 2 𝑎1= 10.
𝑆6 = 630
There will be 360 cells at the
end of 5 minutes.

19. Activity: Test your knowledge.
Find the indicated term sum of each geometric series.
(Page 28)
Assignment: Test your skill.
a. Find the indicated sum of each geometric series.
b. Find the specified value using the given information
about the geometric series.

20. THANK YOU!!!