Latest Capgemini Aptitude Question SOLUTION: The sum of fourth and tenth term of an A.P is 12. Find the sum of the first 13 terms of the progression. (a)78 (b)46 (c)52 (d)None

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(#M40166725) CAPGEMINI Numerical Ability question Keep an EYE

The sum of fourth and tenth term of an A.P is 12. Find the sum of the first 13 terms of the progression.
(a)78 (b)46 (c)52 (d)None

Asked In Capgemini Devendra Marghade (4 years ago)

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Unknown  (4 years ago)

For any Arithmetic Progression, the n'th term can be written as (a + (n-1)d),
where 'a' = first term,
'd' = Common difference between two terms,
'n' = number of terms.
e.g. 1st term = a + 0d = a
2rd term = a+d,
3rd term = a+2d,..and so on.

The sum of the fourth and tenth term of an arithmetic progression is 12.
4th Term + 10th Term = 12
=> (a+3d) + (a+9d) = 12
=> 2a + 12d = 12

Now,,the sum of the first 13 terms of the arithmetic progression is,,,

Sum of n terms of a arithmetic progression is given by ,,
Sum=n(a+l)/2,
where 'n' = number of terms, 'a' = first term, and 'l' = last term

Sum of first 13 terms = 13(1st term+13th term)/2
=> 13(a+(a+12d))/2
=> 13(2a+12d)/2
=> (13)(12)/2
=> 78 is the Answer....

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