Answer: the first term of the series is 128
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
r = 1/4 = 0.25
n = 4
S4 = 170
Therefore, the expression for the sum of the 4 terms, S4 is
170 = a(1 - 0.25^4)/(1 - 0.25)
170 = a(1 - 0.00390625)/(1 - 0.25)
170 = a(0.99609375)/(0.75)
170 = 1.328125a
a = 170/1.328125
a = 128
6s+4d=$53
4s+6d=$47
Multiply 6 in the first equation which is
36s+24d=$318
Multiply -4 in the second equation which is
-16s-24d=$-188
Then..
36s+24d=$318
-16s-24d=$-188
You cancel out the -24d and +24d
36s=$318
-16s=$-188
Do the math..
20s=$130
Divide 20 by both sides and answer...
s=$6.5
Critical points is where the derivative (slope) is zero or does not exist. So to do this we have to find the derivative of our function:

So we apply chain rule:
=

Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1
Carry on... There is not sufficient information to answer