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Arithmetic Progressions

Question
CBSEENMA10007885

Find the sum of the first 40 positive integers divisible by 6.

Solution

The A .P.’s of the first 40 positive integers be 6. 12, 18, 24,......., 40 terms.
Here, a = 6, d = 6, n = 40
We space know space that comma space space straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight g right square bracket
So comma space space space space space space space straight S subscript 49 equals 40 over 2 left square bracket 2 cross times 6 plus left parenthesis 40 minus 1 right parenthesis 6 right square bracket
space space space space space space space space space space space space space space space space space equals 20 left square bracket 12 plus 39 cross times 6 right square bracket
space space space space space space space space space space space space space space space space space equals 20 left parenthesis 12 plus 2340
space space space space space space space space space space space space space space space space space equals space 20 cross times 246
space space space space space space space space space space space space space space space space space equals space 4920.