1. The document discusses geometric sequences and series, including: - Calculating common ratios, terms, and sums - Determining whether sequences converge or diverge - Using formulas to calculate sums of finite and infinite geometric sequences 2. Key formulas presented are for the sum of the first n terms of a geometric sequence and the sum of an infinite geometric sequence. 3. An example problem calculates the total distance travelled by a pendulum where the distance halves each swing.

2. 1. What is the common ratio of the sequence
100, −50,25, −
25
2
?
2. What is the first term of the sequence whose
2nd and 3rd terms are 4 and 16 respectively?
3. What is the 5th term of the geometric
sequence whose 1st term and common ratio are
1
3
and 3 respectively.
4 – 5. What are the missing terms in the
geometric sequence 3, ___,___,375?

3. Marian invested an amount of Php 100,000 to
an account that pays 2% compound interest.
How much will she have on the 5th year?

4. It is the sum of the terms of a geometric
sequence.

5. Find the sum of the first 5 terms of the
geometric sequence 2, 4, 8, …

6. What is the sum of the first 7 terms of a
geometric sequence whose 1st term and
common ratio are 3 and – 2 respectively?

7. The sum of the first n terms of a geometric
sequence is given by
𝑆𝑛 =
𝑎1(1 − 𝑟𝑛
)
1 − 𝑟

8. What is the sum of the first 10 terms of a
geometric sequence whose 1st term and
common ratio are – 2 and 5 respectively?

9. What is the sum of the first 11 terms of a
geometric sequence whose 2nd term and
common ratio are 4 and – 2 respectively?

10. What is the sum of the first 8 terms of a
geometric sequence whose 1st and 8th terms are
1 and 128?

11. What is the sum of the first 8 terms of a
geometric sequence whose 1st and 8th terms are
1 and 128?

12. Divergent Infinite Geometric Sequence
10, 20, 40, 80, 160, 320, …
−10, −20, −40, −80, −160, −320, …
10, −20, 40, −80, 160, −320, …

13. Convergent Infinite Geometric Sequence
100, 50, 25,
25
2
,
25
4
,
25
8
, …
−100, −50, −25, −
25
2
, −
25
4
, −
25
8
, …
100, −50, 25, −
25
2
,
25
4
, −
25
8
, …

14. An infinite geometric sequence whose 0 < 𝑟 <
1. The sum of the terms can be computed.

15. An infinite geometric sequence whose 𝑟 > 1.
The sum of the terms cannot be computed.

16. The sum of the terms of a convergent infinite
geometric sequence is given by the formula
𝑆∞ =
𝑎1
1 − 𝑟

17. A pendulum swings such that the distance it
travels is half the distance it previously
travelled. If on the first swing it travelled a
distance of 32 inches, what is the total distance
it travelled until it totally stops?