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Find the first term and the difference in an arithmetic sequence if the 100th term is 32 and the 200th term is 95.

Find the first term and the difference in an arithmetic sequence if the 100th term-example-1
User Alh
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1 Answer

2 votes

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

User Arnab Bhagabati
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