Question

If 1+2+3+.............n=78 , then the value of n is​

Answer 1

The value of n is 12

Explanation:

We know that the sum of first n term is given by : $S_n=\dfrac{n(n+1)}{2}$

Therefore , if 1+2+3+.............n=78

It means  , $\dfrac{n(n+1)}{2}=78$

Multiply both sides by 2 , we will get

$n(n+1)=156$

$n^2+n-156=0$

$n^2+13n-12n-156=0$

$n(n+13)-12(n+13)=0$

$\Rightarrow\ (n+13)(n-12)=0$

$\Rightarrow\ n= 12\ \&\ n= -13$

Since n is a natural number , so n cannot be negative.

Hence, the value of n is 12.

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