Answer:
364/27
Step-by-step explanation:
9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.
The nth term is a1rn-1.
If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27
32(3-1)n-1 = 3-3
3231-n = 3-3
33-n = 3-3
3-n = -3
n = 6
The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).
So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)
= 9(1 - 1/729) / (2/3)
= (27/2)(728/729) = 364/27
Answer:
true
Step-by-step explanation:
because the variable terms are in the left side of the equation and everything else in right side.
Answer:
x = 1 8/9 or 17/9
Step-by-step explanation:
Step 1: Add 7 to both sides.
Step 2: Divide both sides by 9.
<span>A quadrilateral has congruent diagonals. It is probably a <u>Square</u></span>
The numbers are (-8, 3) or (3, -8).
Step-by-step explanation:
- Step 1: Given the product of the numbers are -24 and their sum are -5. Let the numbers be a and b. Form equations out of these details.
⇒ a + b = -5 ⇒ b = -5 - a
⇒ a × b = -24 -------- (1)
- Step 2: Substitute the value of b in eq(1)
⇒ a × (-5 - a) = - 24
⇒ -5a - a² = -24
⇒ a² + 5a - 24 = 0
- Step 3: Solve the quadratic equation for a.
a = (-5 ± √25 - 4 × 1 × -24)/2
= (-5 ± √121)/2
= - 16/2, 6/2 = -8 or 3
- Step 4: For each value of a, find b.
When a = -8, b = -5 +8 = 3
When a = 3, b = -5 - 3 = -8.
