Two urns each contain green balls and blue balls. Urn I contains 4 green balls and 6 blue balls, and Urn II contains 6 green bal
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The correct answer is C) t₁ = 375, 
.
From the general form,
, we must work backward to find t₁.
The general form is derived from the explicit form, which is
. We can see that r = 5; 5 has the exponent, so that is what is multiplied by every time. This gives us
Using the products of exponents, we can "split up" the exponent:
We know that 5⁻¹ = 1/5, so this gives us
Comparing this to our general form, we see that
Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375
The recursive formula for a geometric sequence is given by
, while we must state what t₁ is; this gives us
From the general form,
The general form is derived from the explicit form, which is
Using the products of exponents, we can "split up" the exponent:
We know that 5⁻¹ = 1/5, so this gives us
Comparing this to our general form, we see that
Multiplying by 5 on both sides, we get that
t₁ = 75*5 = 375
The recursive formula for a geometric sequence is given by
The other number is -3.
Step-by-step explanation:
Step 1; First we develop formulae for the given information. A number is added with 3 and the resulting sum is multiplied by 4. This number is then divided by 2 and the quotient is 0. Assume the unknown number is x, then the given information is as follows
The quotient of is 0. So
= 0.
Step 2; Now we solve the above equation. The denominator is taken to the RHS and the RHS remains zero.
= 0, 4(x+3)= 0, 4x+ 12 = 0, 4x = -12, x =
= -3.
So the other number is -3.