Geometric Sequence and Mean
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The document explains geometric sequences, where each term is derived by multiplying the previous term by a constant called the common ratio. It provides examples demonstrating calculations related to saving money using geometric sequences and finding terms within those sequences. Additionally, it discusses finding geometric means and offers a specific example for inserting geometric means between given numbers.
Geometric Sequence and Mean
- 1. G R O U P T H R E E W A T C H & L E A R N
- 2. I N I T I A L I Z I N G . . .
- 3. A sequence is an ordered list of numbers.
- 4. W E P R O U D L Y P R E S E N T T O Y O U : O M E T R I S E Q U E N C E S A N D E O M E T R I M E A N EG C CG
- 6. When each term in a sequence is found by multiplying the previous term by a constant, it is called Geometric Sequence
- 7. Each term is multiplied by 2 to get the preceding terms. The 1st term (a1)is -1. To obtain the second term, the common ratio (r) is multiplied to a1.
- 8. Tools and Techniques for Quality Improvement a1 a2 = a1r a3 = a2r = (a1r)r = a1r2 a4 = a3r = a1(r)r(r) = a1r3
- 9. Geometric Sequence General Rule 1st term of the sequence Common ratio Number of terms an=a1 .rn-1
- 10. Geometric Sequence EXAMPLES 1 2 3 4 Mr. Rivera wants to save money on his bank account. He decided to double the amount of money that he will deposit every month. He started to save ₱ 100 on his bank account. About how much will he save after 5 months? Given: a1=₱ 100 r = 2 n=5 a5=? Solution: an= a1 .rn-1 a5 = ₱ 100 (2)5-1 a5 = ₱ 100 (2)4 a5 = ₱ 100 (16) a5 = ₱ 1600 Answer: ₱1600
- 11. Geometric Sequence EXAMPLES 1 2 3 4 Given that a1 = -3.5, r = 4 and an = -224, find the value of n. Given: a1=-3.5 r = 4 an=-224 n=? Solution: an= a1 .rn-1 -224=-3.5(4n-1) 64=4n-1 22n-2=26 2n-2=6 2n=6+2 n=4 Answer: 4
- 13. Geometric Mean EXAMPLES 1 2 3 4 Insert 3 geometric mean Between 4 and 1024. Given: a1=4 a5=1024 r=? a2, a3, a4=? Solution: a5=a1rn-1 1024=4r4 256=r4 r=4 a2=4(4) 1=16 a3=4(4) 2=64 a4=4(4) 3=256 =16, 64, 256 Answer: 4, 16, 64, 256, 1024