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Arithmetic Progressions

Question
CBSEENMA10007569

Find the sum of the following APs:
0.6, 1.7, 2.8, . . ., to 100 terms.

Solution

Here a = 0.6
d = 1.7 – 0.6 = 1.1 And, n = 100 We know that,
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 100 equals 100 over 2 left square bracket 2 cross times 0.6 plus left parenthesis 100 minus 1 right parenthesis cross times 1.1 right square bracket
                   
              = 50 x [2 x 0.6 + (100 - 1) x 1.1]
              = 50 x [1.2 + 108.9]
              = 50 x 110.1 = 5505.0 

Hence, the sum of first 100 terms of the given
A.P. = 5505.