the first term of an original sequence is 3,6,9,12,15,... Find the first six terms in each of the following case: 2.The sum of the first two terms of the original sequence is 7
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To find the first six terms of the sequence where the sum of the first two terms is 7, we need to determine the pattern between consecutive terms and use it to generate the sequence.
Let's start by examining the original sequence: 3, 6, 9, 12, 15, ...
To find the pattern between consecutive terms, we subtract the current term from the next term. We can observe that each term increases by 3: 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3, 15 - 12 = 3, ...
So, the pattern between consecutive terms is that each term increases by 3.
Now, since the sum of the first two terms of the sequence is 7, we can write the equation:
First term + Second term = 7
Let's substitute the first term as 3:
3 + Second term = 7
To find the value of the second term, we subtract 3 from both sides:
Second term = 7 - 3 = 4
Now, using the pattern we found earlier (each term increases by 3), we can generate the first six terms of the sequence:
First term = 3
Second term = 4
Third term = Second term + 3 = 4 + 3 = 7
Fourth term = Third term + 3 = 7 + 3 = 10
Fifth term = Fourth term + 3 = 10 + 3 = 13
Sixth term = Fifth term + 3 = 13 + 3 = 16
Thus, the first six terms of the sequence where the sum of the first two terms is 7 are:
3, 4, 7, 10, 13, 16.