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
Answer:
A ≈ $500
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Compounded Interest Rate: A = P(1 + r/n)ⁿˣ
- A is final amount
- P is initial (principle) amount
- r is rate
- n is number of compounds
- x is number of years
Step-by-step explanation:
<u>Step 1: Define</u>
P = 230
r = 0.063
n = 365
x = 12
<u>Step 2: Solve for </u><em><u>A</u></em>
- Substitute: A = 230(1 + 0.063/365)³⁶⁵⁽¹²⁾
- Divide: A = 230(1 + 0.000173)³⁶⁵⁽¹²⁾
- Multiply: A = 230(1 + 0.000173)⁴³⁸⁰
- Add: A = 230(1.00017)⁴³⁸⁰
- Exponents: A = 230(2.1296)
- Multiply: A = 489.808
Answer:
-5.5
Step-by-step explanation:
Answer:
x = 53
Step-by-step explanation:
Remember that the sum of all 3 interior angles in a triangle is 180∘ so
74 + x + x = 180
74 + 2x = 180
2x = 180 - 74
2x = 106
x = 106/2
x = 53
0.017779534 because you just divide it
