Answer:
Explanation:
To find the first six terms of the original sequence, we can use the given first difference sequence.
a. If the first term of the original sequence is 3, we can start by adding the first difference to this term repeatedly to get the subsequent terms.
So, the first six terms of the original sequence are:
3, 5, 8, 11, 14, 17
b. If the sum of the first two terms in the original sequence is 12, we can set up an equation to find the first two terms. Let's assume the first term is x. Then the second term would be (12 - x).
Using the given first difference, we can find the remaining terms. Adding the first difference to the second term repeatedly, we get the subsequent terms.
So, the first six terms of the original sequence are:
4, 8, 11, 14, 17, 20
c. If the fifth term in the original sequence is 34, we can find the value of the first term using the first difference. Subtracting the first difference four times from the fifth term, we can find the first term.
Then, using the first difference, we can find the remaining terms.
So, the first six terms of the original sequence are:
-1, 2, 5, 8, 11, 14
In all three cases, the first six terms of the original sequence are:
3, 5, 8, 11, 14, 17 (in ascending order).