Answered

Write out the first 3 values for the summation ∑[tex]\frac{45}{n=1}[/tex] (3n-2). Then calculate the complete sum by rewriting it using the arithmetic sum formula.



Answer :

Answer:

  • the first 3 values = 1, 4, 7
  • the sum = 3015

Step-by-step explanation:

To find the first 3 values for the summation, just substitute the variable n with {1, 2, 3}:

[tex]\boxed{U_n=3n-2}[/tex]

  • [tex]U_1=3(1)-2=1[/tex]
  • [tex]U_2=3(2)-2=4[/tex]
  • [tex]U_3=3(3)-2=7[/tex]

Therefore, the first 3 values are {1, 4, 7}

From the question and the 3 values above, we can find that:

  • [tex]n=45[/tex]
  • [tex]U_1=1[/tex]
  • [tex]d=U_2-U_1=4-1=3[/tex]

To find the sum of this arithmetic sequence, we can use the arithmetic sum formula:

[tex]\boxed{S_n=\frac{n}{2} (U_1+U_n)}[/tex]

First we have to find the [tex]U_n[/tex] in order to calculate the sum.

[tex]U_n=3n-2[/tex]

[tex]U_{45}=3(45)-2[/tex]

[tex]U_{45}=133[/tex]

Now, we can find the sum:

[tex]\begin{aligned} S_n&=\frac{n}{2} (U_1+U_n)\\\\&=\frac{45}{2}(1+133)\\\\&=\bf 3015 \end{aligned}[/tex]

Other Questions