The 12th term in the sequence is -26.
Given,
B (n) = -4 – 2(n – 1)
We have to find the 12th term in the sequence:
To find the nth term in an arithmetic sequence:
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.
Here,
First term, a = -4
Common difference, d = -2
nth term = 12
Now, let’s find 12th term
B(n) = -4 -2(n – 1)
B(12) = -4 – 2(12 – 1)
B(12) = -4 -2(11)
B(12) = -4 -22
B(12) = -26
That is, the 12th term in the sequence is -26.
Learn more about arithmetic sequence here:
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First, you need to rewrite the expression into binomial form, so you are working with two terms (as you world with a quadratic):
(x²)²-3(x²)-4=0
Now, you can place the x²s into brackets as the coefficient is now 1:
(x² )(x² )
Next, find out two numbers that add together to give you -3 and multiply to give -4 (these are the leftover integers after removing the x²s). These two numbers are -4 and 1.
Place the -4 and 1 into the brackets:
(x²-4)(x²+1)=0
Notice that the x²-4 is a difference of two squares, so can be further factorised into (x+2)(x-2)
This leaves you with a final factorisation of:
(x+2)(x-2)(x²+1)=0
Now we handle each bracket individually to obtain our four solutions for x:
x+2=0
x=-2
x-2=0
x=2
x²+1=0
x²=1
x=<span>±1</span>
1.2 of the blue candies were damaged. Out of the 60 candies, 18 were orange (0.3 x 60) and 18 were green (0.3 x 60). 12 of the candies were red (0.2 x 60) and 12 were blue (0.2 x 60). 1.2 of these 12 blue candies were damaged (0.1 x 12).
