To find the first six terms of the sequence defined by a1 = 7 and an = an-1 + 6, we can start with the first term and use the recursive formula to calculate the subsequent terms.
- First term (a1): Given as 7.
- Second term (a2): Using the formula, a2 = a1 + 6 = 7 + 6 = 13.
- Third term (a3): a3 = a2 + 6 = 13 + 6 = 19.
- Fourth term (a4): a4 = a3 + 6 = 19 + 6 = 25.
- Fifth term (a5): a5 = a4 + 6 = 25 + 6 = 31.
- Sixth term (a6): a6 = a5 + 6 = 31 + 6 = 37.
The first six terms of the sequence are:
- a1 = 7
- a2 = 13
- a3 = 19
- a4 = 25
- a5 = 31
- a6 = 37
This sequence increases linearly by 6 for each term after the first. The pattern is clear, and the formula allows for easy computation of subsequent terms.