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The first and last terms of an Arithmetic progression (AP) are -3 and 393 respectively. If the progression has 100 terms, find the 33rd term of the AP.
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3 stepsIdentify the given values and the formula for the -th term of an Arithmetic Progression (AP).
The first term, .
The last term, .
The total number of terms, .
The formula for the -th term is , where is the common difference.Use the last term to find the common difference ().
The last term is the 100th term, so .
Substitute the values into the formula:Add 3 to both sides:
Divide by 99 to find :
Calculate the 33rd term ().
Now that we have the common difference , we can find the 33rd term using the formula with .
The 33rd term of the AP is .
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