Final answer:
To find the first five terms of the given arithmetic sequence, calculate the common difference and then use it to determine each subsequent term. The terms are 4.5, 5.0, 5.5, 6.0, and 6.5.
Step-by-step explanation:
To write the first five terms of the arithmetic sequence with the given values a_1=4.5, and a_5=6.5, we need to first find the common difference (d). The formula to find the nth term of an arithmetic sequence is:
a_n = a_1 + (n-1)d
We can use the formula and the given term a_5 to find the common difference:
6.5 = 4.5 + (5-1)d
Solving for d gives us:
d = (6.5 - 4.5) / 4
d = 0.5
Now we have the common difference, we can write the first five terms of the sequence:
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- a_1 = 4.5
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- a_2 = 4.5 + 0.5 = 5.0
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- a_3 = 5.0 + 0.5 = 5.5
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- a_4 = 5.5 + 0.5 = 6.0
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- a_5 = 6.0 + 0.5 = 6.5