Answer:
d = 0.63
Step-by-step explanation:
The equation for the nth term in an arithmetic sequence is
an = a + (n-1)d
Where a is the first term and d is a common difference.
We know that the 100th term is 32 and the 200th term is 95, so we can write the following equations
32 = a + (100 - 1)d
32 = a + 99d
95 = a + (200 - 1)d
95 = a + 199d
If we solve the first equation for a, we get
32 = a + 99d
32 - 99d = a + 99d - 99d
32 - 99d = a
Then, replace a = 32 - 99d on the second equation and solve for d
95 = a + 199d
95 = 32 - 99d + 199d
95 = 32 + 100d
95 - 32 = 32 + 100d - 32
63 = 100d
63/100 = 100d/100
0.63 = d
Therefore, the difference in the arithmetic sequence is 0.63