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Arithmetic Progressions

Question
CBSEENMA10007567

Find the sum of the following APs:
2, 7, 12, ... to 10 terms.

Solution

Here, a = 2
d = 7 – 2 = 12 – 7 = 5
And, n = 10
We know that,
space space space space 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 d right square bracket
therefore space space straight S subscript 10 equals 10 over 2 left square bracket 2 cross times 2 plus left parenthesis 10 minus 1 right parenthesis cross times 5 right square bracket
          = 5 x [4 + 9 x 5]
          = 5 x [4 + 45]
          = 5 x 49 = 245

Hence, the sum of First 10 terms of the given
A .P. = 245 F