I'll do problem 13 to get you started.
The expression
is the same as 
Then we can do a bit of algebra like so to change that n into n-1

This is so we can get the expression in a(r)^(n-1) form
- a = 8/7 is the first term of the geometric sequence
- r = 2/7 is the common ratio
Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).
We'll plug those a and r values into the infinite geometric sum formula below
S = a/(1-r)
S = (8/7)/(1 - 2/7)
S = (8/7)/(5/7)
S = (8/7)*(7/5)
S = 8/5
S = 1.6
------------------------
Answer in fraction form = 8/5
Answer in decimal form = 1.6
not sure what your asking..don’t think you can identify what “t” is without further explanation!
Answer:
13x + 7 = 5x - 20
Step-by-step explanation:
SOLVE for X
13x + 7 = 5x - 20
-------------------------
-5x -7
------------------------
8x=-27
x= -3.375 or -27/8
Answer:
The value of x is 12.
Step-by-step explanation:
To make the denominators the same we can: Multiply the top and bottom of each fraction by the denominator of the other.

Cross multiply with each other.

The algebraic solution to the situation is as follows:
x + y = 750
10x + 6y = 6860
The number of adult and student are 590 and 160 respectively.
<h3>How to find and solve an algebraic equation?</h3>
One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.
One evening,750 people attended the play and the total receipts were 6860.
Therefore,
let
x = number of adult ticket
y = number of student tickets
Therefore,
x + y = 750
10x + 6y = 6860
10x + 10y = 7500
10x + 6y = 6860
4y = 640
y = 640 / 4
y = 160
Hence,
x = 750 - y
x = 750 - 160
x = 590
learn more on algebraic expression here: brainly.com/question/14934521
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