Answer:
243 inches squared
Step-by-step explanation:
1) The total perimeter for each part is 8x.
2) 72 divided by 8 = 9
3) height = 9 base = 27
4) 9 x 27 = 243 inches squared
Your money grows faster because the interest is added back into the principle and then the next time it compounds you get interest on the new principle amount. So for example, you deposit $100 in an account that gets 5% interest compounded semiannually. The first time it compounds you get $5 added to your account so your new balance is $105. The next time it compounds you get 5% on $105 so you get $5.25 added and so on. If this is only happening semi-annually that would be all you get for the year. But if it happens quarterly you would get would get deposits of $5.51 and $5.79 as well. If it compounds monthly or even daily your money would grow more and more. Hope this helps.
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
