Final answer:
The 63rd term of the arithmetic sequence with the 7th term being 23 and a common difference of -0.3 is 6.2.
Step-by-step explanation:
To find the 63rd term of an arithmetic sequence when the 7th term is 23 and the common difference d is -0.3, we use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n-1)d
First, we need to find the first term of the sequence (a1). We know the 7th term (a7) is 23. We plug this value into the formula and solve for a1:
23 = a1 + (7-1)(-0.3)
This simplifies to:
23 = a1 + 6(-0.3)
23 = a1 - 1.8
Therefore, a1 = 23 + 1.8 = 24.8
Now, we'll find the 63rd term (a63) using a1 and d:
a63 = 24.8 + (63-1)(-0.3)
This simplifies to:
a63 = 24.8 + 62(-0.3)
a63 = 24.8 - 18.6 = 6.2
So, the 63rd term of the sequence is 6.2.