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

Answers (1)
D Deependra Verma

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

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