SOLUTION: Given that the 2rd term of a G.p is 180 and the 3rd term is 360, calculate: a) the first term b) the common ratio c) the sum of the first four terms

Question 1204435: Given that the 2rd term of a G.p is 180 and the 3rd term is 360, calculate:
a) the first term
b) the common ratio
c) the sum of the first four terms
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The two consecutive terms tells you common ratio is . From this you can figure out the rest.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll start with part (b).
To get the common ratio, we divide any given term over its previous one.

r = common ratio
r = term3/term2
r = 360/180
r = 2
The common ratio is 2.

We know the 2nd term is 180.
To get to the third term, we multiply by r = 2.
To go backwards to the first term, we divide by the common ratio.

term1 = term2/r
term1 = 180/2
term1 = 90

Notice that the first equation can be rearranged into r = term2/term1.

We know the first three terms are 90, 180, 360.
The fourth term is 720 since we double 360 to get there.
Then adding those four terms gets us: 90+180+360+720 = 1350

Or we can use this formula
Sn = sum of the first n terms of a geometric progression (GP)
Sn = a*(1 - r^n)/(1 - r)
S4 = 90*(1 - 2^4)/(1 - 2)
S4 = 1350

Side note: The nth term of this GP is 90*(2)^(n-1)

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Summary
(a) first term = 90
(b) common ratio = 2
(c) sum of first four terms = 1350

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