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# Geometric Sequence and Mean

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Marx Del Mundo
Angel Mae Ruiz
Reenie Trisha Vergara

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### Geometric Sequence and Mean

1. 1. G R O U P T H R E E W A T C H & L E A R N
2. 2. I N I T I A L I Z I N G . . .
3. 3. A sequence is an ordered list of numbers.
4. 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
5. 5. Geometric Sequence Geometric Mean
6. 6. When each term in a sequence is found by multiplying the previous term by a constant, it is called Geometric Sequence
7. 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. 8. Tools and Techniques for Quality Improvement a1 a2 = a1r a3 = a2r = (a1r)r = a1r2 a4 = a3r = a1(r)r(r) = a1r3
9. 9. Geometric Sequence General Rule 1st term of the sequence Common ratio Number of terms an=a1 .rn-1
10. 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. 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
12. 12. Geometric Mean RatioFormula
13. 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