the first number of a sequence is 200. every number of the sequence after the first is 100 less than twice the preceding number. what is the 5th number of the sequence
t1 = 200
t2 = 2t1 -100 = 2(200) - 100 = 300
t3 = 2t2 - 100 = 2(300) - 100 = 500
t4 = ...
..
t6 = 2t5 - 100 = ...
(you should get 3300)
oops, went too far, only had to go to t5
how about 1700 ?
To find the 5th number of the sequence, we need to use the given information that the first number is 200 and each subsequent number is 100 less than twice the preceding number.
Let's break down the problem step by step:
1. The first number is given as 200.
Therefore, the first term of our sequence is 200.
2. Each subsequent number is 100 less than twice the preceding number.
Let's derive the formula for the nth term of the sequence:
- First term: 200
- Second term: (2 * preceding term) - 100
- Third term: (2 * second term) - 100
- Fourth term: (2 * third term) - 100
- Fifth term: (2 * fourth term) - 100
3. Now, we can calculate the fifth term of the sequence using the formula:
Let's substitute the values to find the fifth term:
Fifth term = (2 * fourth term) - 100
Fifth term = (2 * [(2 * third term) - 100]) - 100
Fifth term = (2 * [(2 * [(2 * second term) - 100]) - 100]) - 100
Fifth term = (2 * [(2 * [(2 * [(2 * 200) - 100]) - 100]) - 100]) - 100
Simplifying the above expression will give us the fifth term of the sequence.
Now, let's calculate the fifth term:
1. (2 * 200) - 100 = 400 - 100 = 300
2. (2 * 300) - 100 = 600 - 100 = 500
3. (2 * 500) - 100 = 1000 - 100 = 900
4. (2 * 900) - 100 = 1800 - 100 = 1700
5. (2 * 1700) - 100 = 3400 - 100 = 3300
Therefore, the fifth number of the sequence is 3300.