Question

If the first term of an arithmetic sequence is 203 and the 30th term of the sequence is 261 , find the sum of the first 1000 terms.

Answer 1

To find the sum of the first 1000 terms of an arithmetic sequence, we first need to find the common difference between the terms. Next, we can use the formula for the sum of an arithmetic sequence and evaluate the expression to find the sum.

Step-by-step explanation:

To find the sum of the first 1000 terms of an arithmetic sequence, we first need to find the common difference between the terms. We can do this by subtracting the first term from the 30th term:

Common difference = 261 - 203 = 58

Next, we can use the formula for the sum of an arithmetic sequence:

Sum = (n/2)(first term + last term)

Plugging in the values:

Sum = (1000/2)(203 + (203 + (1000 - 1) * 58))

Finally, we can evaluate this expression to find the sum of the first 1000 terms.