IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 2 : The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + . . is

Video Explanation

Explanatory Answer

1*3 + 5*7 + 9*11 …..
Here we can see that in the first term of the series, the number is of the form (2 - 1)*(2 + 1)
Or (2² - 1²)
And the second term is of the form (6 - 1)*(6 + 1),
Or (6² - 1²)
So the terms also make a series where the common difference is 4. The 10^th term can be found to be
[first term + (n - 1)(common difference)]
= [2 + 9*4]
= 38
So the 10th term in the series can be rewritten as (38² - 1²)
In the series we are adding 2² + 6² + 10² + … + 38² and subtracting 1 for each term
Which is 2² + 6² + 10² + … + 38² - 10
= 4[1² +3² +5² …..19² ] - 10
= 4[1330] -10
5310

The question is " The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + . . is "

Hence, the answer is '5310'

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