I have one question I really need help with. I know the partial sum process but my numbers don't seem to come out to what I think it should be.
Find the partial sum S6
1. An=3n+2
To find the partial sum S6 of the sequence An=3n+2, you need to substitute the values of n from 1 to 6 into the formula and then add them up. Here's how you can do it step-by-step:
Step 1: Write out the first six terms of the sequence:
A1 = 3(1) + 2 = 5
A2 = 3(2) + 2 = 8
A3 = 3(3) + 2 = 11
A4 = 3(4) + 2 = 14
A5 = 3(5) + 2 = 17
A6 = 3(6) + 2 = 20
Step 2: Add up the terms:
S6 = A1 + A2 + A3 + A4 + A5 + A6
= 5 + 8 + 11 + 14 + 17 + 20
Step 3: Calculate the sum:
S6 = 75
Therefore, the partial sum S6 of the sequence An=3n+2 is 75.
To find the partial sum S6 for the sequence An = 3n + 2, we need to understand the concept of a partial sum.
The partial sum S6 represents the sum of the first six terms of the sequence. In other words, we need to find the sum of A1, A2, A3, A4, A5, and A6.
To find each term of the sequence, we can substitute values of n into the given formula An = 3n + 2. Let's calculate the first six terms:
A1 = 3(1) + 2 = 3 + 2 = 5
A2 = 3(2) + 2 = 6 + 2 = 8
A3 = 3(3) + 2 = 9 + 2 = 11
A4 = 3(4) + 2 = 12 + 2 = 14
A5 = 3(5) + 2 = 15 + 2 = 17
A6 = 3(6) + 2 = 18 + 2 = 20
Now that we have found the first six terms, we can calculate the partial sum S6 by adding them together:
S6 = A1 + A2 + A3 + A4 + A5 + A6
= 5 + 8 + 11 + 14 + 17 + 20
= 75
Therefore, the value of the partial sum S6 for the sequence An = 3n + 2 is 75.