Question

If 1+4 +7 +10+ ... + x = 287, find the value of x.​

Answer 1

Answer:

40

Step-by-step explanation:

Let the number of terms be n

=> $S_n = 287$

=> $\frac{n}{2}[2(1)+(n-1)3]=287$

=> $n(2+3n-3)=574$

=> $n(3n-1)=574=3n^{2}-n$

=> $3n^{2}-n-574=0$

=> n = 14 or -41/3 (I hope that you can solve the equation)

Since -41/3 can't be the number of terms, n = 14

Now you know the number of terms, u can find x

x = 1 + (14 - 1)3 = 1 + 13*3 = 1 + 39 = 40

Hence proved.

Thank you.

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