Good day everyone, my name is Alvin Joel Partezan. I am the student of Mount Laumit Sangguansang from Greater Aginado. So now, I am going to discuss the geometric sequence and how to solve the geometric sequence.
What is geometric sequence? It is a sequence where each term is obtained by multiplying the previous term by a constant number. A constant number is called a common ratio.
denoted by the symbol of r. The formula of the ratio is r equals to a sub 2 over a sub 1. And the formula of the geometric sequence is a sub n equals to a sub 1 ratio m2 minus 1. Example. So, the geometric sequence. Example number 5. Find the sixth term of a sequence 2, 6, 13, 16, 17. so first we use the formula of the ratio how to solve the ratio so first is what is the value of a2 the a2 is this the a2 is 6 over the a1 is 2 so 2 so 6 divided by 2 I'm your host, Tuyen. Our ratio is 3. So, 2 times 3 equals to 6. 6 times 3 equals to 18. 18 times 3 equals to 54. 54 times 3 equals to 162. 162 times 3 is 486. Given the sequence of 2, 6, 18, 54, 162, and 486. So what is the 10th term?
So the given is a1 is 2 and the nth term is 2. is 10 our ratio is 3 we use the geometric sequence or geometric formula the end the end is 10 equals a sub 1 and the ratio is 3 copy the end which is the 10 minus one bring down a sub 10 and 2 open parentheses 3 close part 10 minus 1 is 9 bring down 8 times 10 equals 2 bring down 2 so how to solve this so the tree is multiplied by itself with 9 so 33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 19,680. So, bring down 10. 2 times 19,683 is equal to 39,366. Our ASAP 10 is 39,366.
Another example. Find the fifth term of the sequence 3, 6, and 12. So first we do is find the common ratio. The common ratio is r equals to a sub 2 over a sub 1, sub 2. One ratio is 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24, 24 times 2 is 40. Given the sequence of 3, 6, 12, 24, and 28. So first the given, ang A sub 1 is 3 and the n-term is 8. Our ratio is 2. So, the formula of the geometric sequence is a sub n plus e sub 1 common ratio raised to the power of n minus 1. So, substitute the a.
The n-term is 8 equals to a sub 1 is 3. Our ratio is 2. So, the n is 8 minus 1. So, bring down a sub n equals bring down 3. Close open parenthesis, 2 close parenthesis. 8 minus 1 is 7. So, how to solve this? So, the 2 is multiplied by itself with 7 for example.
2 x 128 so bring down 8 equals 3 times 128 is 384 so this is the final result our a sub 8 is 384 thanks for watching don't forget to like and share