Final answer:
To find the missing terms in the arithmetic sequence with the first term 7 and last term 39, calculate the common difference by dividing the total difference between the first and last terms by the number of terms minus one. In this case, the common difference is 8, enabling us to find the full sequence: 7, 15, 23, 31, 39.
Step-by-step explanation:
To find the missing terms in the arithmetic sequence 7, ____ ,____ , _____ , 39, we must first determine the common difference between each term. Since we know the first term (7) and the last term (39), we can find the common difference by calculating the difference between them and dividing it by the number of gaps in the sequence. There are four gaps (three missing terms), so we will divide the overall difference by four.
First, calculate the difference between the first and last terms: 39 - 7 = 32. Then divide this difference by the number of gaps (four): 32 ÷ 4 = 8. Thus, the common difference in this sequence is 8.
Now that we have the common difference, we can add it to the first term to find the second term, and then continue adding it to each subsequent term to find the others. Let's apply this method:
- Add 8 to the first term (7): 7 + 8 = 15. So, the second term in the sequence is 15.
- Add 8 to the second term (15): 15 + 8 = 23. The third term in the sequence is 23.
- Add 8 to the third term (23): 23 + 8 = 31. The fourth term is 31.
Now we have filled in the blanks, and our complete sequence is: 7, 15, 23, 31, 39.