Question 1204435
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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
<font color=red>r = 2
The common ratio is 2.</font>


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
<font color=red>term1 = 90</font>


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 = <font color=red>1350</font>



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 = <font color=red>1350</font>



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


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Summary
(a) first term = <font color=red>90</font>
(b) common ratio = <font color=red>2</font>
(c) sum of first four terms = <font color=red>1350</font>
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