I have 3 questions I'm stuck on and would love for someone to explain and show me how to solve them so I can also solve the other one.


Find the partial sum S6
1. An=3n+2

2. Find the number of terms n in an arithmetic sequence if a1=20, d=5, and An=75.

3. Find the general term for 8,17,26,35,44......

3. 8, 8*2+1, 8*3+2, 8*n+n-1

or An=9n-1

3. x + 9

#2

Term(n) = a+(n-1)d

75 = 20 + (n-1)(5)
55 = 5(n-1)
11 = n-1
n = 12

there are 12 terms

Thanks for the help bobpursley and Reiny I appreciate showing how you got to it so I can also do it.

Sure, I can help you with that! Let's go through each question step by step.

1. To find the partial sum S6 for the sequence An = 3n + 2, we need to add up the first 6 terms of the sequence.

First, let's find the values of the first 6 terms:
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

Now, we'll add up these terms:
S6 = A1 + A2 + A3 + A4 + A5 + A6
= 5 + 8 + 11 + 14 + 17 + 20
= 75

Therefore, the partial sum S6 for the sequence An = 3n + 2 is 75.

2. To find the number of terms n in an arithmetic sequence, where a1 = 20, d = 5, and An = 75, we can use the formula for the general term of an arithmetic sequence and solve for n.

The formula for the nth term of an arithmetic sequence is An = a1 + (n-1)d.

Substituting the given values, we have:
75 = 20 + (n-1)5

Simplifying the equation:
75 = 20 + 5n - 5
75 - 20 + 5 = 5n
60 = 5n
n = 60/5
n = 12

Therefore, the number of terms n in the arithmetic sequence is 12.

3. To find the general term for the sequence 8, 17, 26, 35, 44..., we observe that each term increases by 9. Therefore, the common difference (d) between consecutive terms is 9.

Now let's consider the first term, which is 8. We can see that this term is 8 more than a multiple of 9 (8 = 9*0 + 8).

To find the general term, we can use the formula An = a1 + (n-1)d, where An represents the nth term, a1 is the first term, and d is the common difference.

Substituting the values:
An = 8 + (n-1)9
An = 8 + 9n - 9
An = 9n - 1

Therefore, the general term for the sequence 8, 17, 26, 35, 44... is An = 9n - 1.

By understanding these solutions and the steps involved, you'll be able to apply the same concepts to solve other similar problems. I hope this explanation helps!