Final answer:
The 8th term (a_8) of the geometric sequence is 411771.5, found by successively multiplying each term by 7.
Step-by-step explanation:
The sequence provided: 0.5, 3.5, 24.5, 171.5 appears to be a geometric sequence where each term is seven times the previous term. To find the 8th term (a8) of the sequence, we would multiply the 7th term by 7.
- First term (a1): 0.5
- Second term (a2): 3.5 = 0.5 × 7
- Third term (a3): 24.5 = 3.5 × 7
- Fourth term (a4): 171.5 = 24.5 × 7
To find a8, we continue this pattern:
- a5 = a4 × 7 = 171.5 × 7 = 1200.5
- a6 = a5 × 7 = 1200.5 × 7 = 8403.5
- a7 = a6 × 7 = 8403.5 × 7 = 58824.5
- a8 = a7 × 7 = 58824.5 × 7 = 411771.5
Therefore, the 8th term of the sequence is 411771.5.