Look at these two sequences:
2,5,8,11,14
3,6,9,12,15
Will these two sequences ever have a term in common. Give a reason for your answer
Yes, these two sequences will have a term in common. The reason is that both sequences have a common difference of 3. This means that if we keep adding 3 to each term in both sequences, eventually we will arrive at the same number. In this case, if we add 3 three times to the first sequence, we get 14 + 3 + 3 + 3 = 23. And if we add 3 twice to the second sequence, we get 15 + 3 + 3 = 21. Therefore, the sixth term of the first sequence (23) and the fifth term of the second sequence (21) are the same, so the two sequences have a term in common.
21 and 23 aren’t the same number
Apologies for the mistake. You are correct, 21 and 23 are not the same number. Therefore, in this case, the two sequences do not have a term in common. Since the two sequences have a common difference of 3, the terms in both sequences will always be three numbers apart. Thus, it is not possible for any term in the first sequence to be equal to a term in the second sequence.
Can you explain that again
Apologies for the confusion. Let's analyze the sequences again:
Sequence 1: 2, 5, 8, 11, 14
Sequence 2: 3, 6, 9, 12, 15
Upon closer inspection, we can see that the terms in both sequences are increasing by a common difference of 3. In other words, we add 3 to each term to get the next term in each sequence.
Now, to determine if these two sequences will ever have a term in common, we need to check if there is any number that exists in both sequences simultaneously.
We can start by comparing the first terms: 2 (from Sequence 1) and 3 (from Sequence 2). As you can see, these two terms are not the same.
Next, let's compare the second terms: 5 (from Sequence 1) and 6 (from Sequence 2). Again, these terms are not the same.
Continuing this process, we compare the third terms: 8 (from Sequence 1) and 9 (from Sequence 2). Once again, these terms are not equal.
We can continue this analysis for the remaining terms, and we will see that each term in Sequence 2 is exactly 1 greater than the corresponding term in Sequence 1.
Therefore, these two sequences will never have a term in common because the terms in both sequences always differ by 1, and they will keep getting farther apart as the sequences progress.