Explanation:
Let's analyze the information given:
a. The first difference of the sequence is 2, 5, 8, 11, 14.
To find the first six terms of the original sequence, you can start with the first term, which is given as 3, and then add the corresponding differences successively:
1st term: 3
2nd term: 3 + 2 = 5
3rd term: 5 + 5 = 10
4th term: 10 + 8 = 18
5th term: 18 + 11 = 29
6th term: 29 + 14 = 43
So, the first six terms of the original sequence are 3, 5, 10, 18, 29, and 43 (in ascending order).
b. The sum of the first two terms in the original sequence is 12.
We already found that the first term is 3. To find the second term, you can subtract the first difference (2) from the second term:
2nd term = 3 + 2 = 5
Now, check if the sum of the first two terms is 12:
3 + 5 = 8 (not 12)
The sum of the first two terms is not 12; it's 8.
c. The fifth term in the original sequence is 34.
We already calculated the first five terms of the original sequence, and the fifth term is 29, not 34.
So, to summarize:
a. The first six terms of the original sequence are 3, 5, 10, 18, 29, and 43.
b. The sum of the first two terms in the original sequence is 8.
c. The fifth term in the original sequence is 29.