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CAT 2019 Slot 2 QA Question & Solution

AlgebraMedium

Question

If $(2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280$, then whatis the value of $1 + 2 + 3 + .. + n?$

Solution

Let us first find the number of terms 

47=1+(n-1)2

n=24

24*2n+1+3+5+....47=5280

48n+576=5280

48n=4704

n=98

Sum of first 98 terms = 98*99/2

=4851