Solve the solution 1+4+7+10.............+x = 287

Name: Solve the solution 1+4+7+10.............+x = 287
Uploaded: Mon, 2021-05-31 13:58
Description: Solve the solution 1+4+7+10.............+x = 287

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Solve the solution 1+4+7+10.............+x = 287

Answers (1)

Here,
a=1,d=4-1=3 and let S(n)=n
Let n be the number of terms.
We know the formula:
$S_n=fracn2[2a(n-1)d]$
Putting all the values we get,
$Rightarrow 287=fracn2[2*1+(n-1)3]$
$Rightarrow 287=fracn2[2+(n-1)3]$
$Rightarrow 574=3n^2-n$
$Rightarrow 3n^2-n-574=0$
$Rightarrow 3n^2-42n+41n-574=0$
$Rightarrow 3n(n-14)+41(n-14)=0$
$n=14,frac-413$
But n cannot be negative
So the final value of n is $14$
We know that:-
$a+(n-1)d=x$
$Rightarrow 1+(14-1)(3)=x$
$Rightarrow 1+13(3)=x$
$Rightarrow x=40$
Hence the value of x is 40