Question

Write the terms of the series and find their sum.

Answer 1

\[\sum_{k = 1}^{4}(k + 5)^2\]

k = 1, n = 4

\[(1 + 5)^2 = 6^2 = 36\]

Answer 2

Not sure where to go from here....

Answer 3

$$\sum_{k=1}^4(k+5)^2$$First, we're going to write out the terms from \(k=1\) to \(4\) and then we'll manually add them up:$$k=1\colon (1+5)^2=6^2=36\\k=2\colon(2+5)^2=7^2=49\\k=3\colon(3+5)^2=8^2=64\\k=4\colon(4+5)^2=9^2=81$$So then our sum is just:$$\sum_{k=1}^4(k+5)^2=36+49+64+81=230$$

Answer 4

thanks! Thats where I was thinking of going but was not sure if I should start from one and go until 4, again thanks.

Answer 5

it asks what the terms of the series are: it would be 36, 49, 64, and 81, correct? @oldrin.bataku

Answer 6

Indeed they are @angelina22309 .

Answer 7

Do I need to write it out like you did or could I just put

\[\sum_{k = 1}^{4}(k + 5)^2 = 230\]

Answer 8

@oldrin.bataku

Answer 9

@angelina22309 it's up to you and your teacher.