To find the sum of the sequence [tex]\(\sum_{k=1}^5(5k - 3)\)[/tex], let's evaluate each term in the sequence and then add them together.
1. For [tex]\(k = 1\)[/tex]:
[tex]\[
5(1) - 3 = 5 - 3 = 2
\][/tex]
2. For [tex]\(k = 2\)[/tex]:
[tex]\[
5(2) - 3 = 10 - 3 = 7
\][/tex]
3. For [tex]\(k = 3\)[/tex]:
[tex]\[
5(3) - 3 = 15 - 3 = 12
\][/tex]
4. For [tex]\(k = 4\)[/tex]:
[tex]\[
5(4) - 3 = 20 - 3 = 17
\][/tex]
5. For [tex]\(k = 5\)[/tex]:
[tex]\[
5(5) - 3 = 25 - 3 = 22
\][/tex]
Now, we sum these results:
[tex]\[
2 + 7 + 12 + 17 + 22
\][/tex]
We can add these step-by-step:
[tex]\[
2 + 7 = 9
\][/tex]
[tex]\[
9 + 12 = 21
\][/tex]
[tex]\[
21 + 17 = 38
\][/tex]
[tex]\[
38 + 22 = 60
\][/tex]
Therefore, the sum of the sequence is:
[tex]\[
\sum_{k=1}^5(5k - 3) = 60
\][/tex]
