I need some help with algebra I'm not sure how to get to the answer.

Question

Find the number of terms in each sequence.

1. a1=4 an=42 d=2

2. a1--0.3 an=-36 d=2.1

3. 1/12, 1/8, 1/6, 5/24, 1/4,......9/8

Evaluate each sum.

1. There is an e like symbol that has a 15 on top on the bottom n=4 and to the right (3-5n)

Answer 1

since An = A1 + (n-1)d,
42 = 4+(n-1)*2
n=20
So, A20 = 42

This must have a typo, since you can't get to -36 with a positive difference between terms. Assuming you meant d = -2.1,

-36 = -.3 + (n-1)(-2.1)
A18 = -36

Apparently d = 1/24
9/8 = 1/12 + (n-1)(1/12)
A26 = 9/8

15
∑ (3-5n)
4

This just means to add up all the values, substituting in n=4,5,6,...,15

That means add up the sum

-17 + -22 + ... + -72

Answer 2

Thank you this was very helpful!