= 1455
generate a few terms of the sequence using = 3n + 2
= ( 3 × 1) + 2 = 5
= (3 × 2) + 2 = 8
= (3 × 3 ) + 2 = 11
= (3 × 4 ) + 2 = 14
= ( 3 × 5 ) + 2 = 17
the terms are 5, 8, 11, 14, 17
these are the terms of an arithmetic sequence
sum to n terms is calculated using =
[ 2a + (n-1)d]
where a is the first term and d the common difference
d = 8 - 5 = 11 - 8 = 14 - 11 = 3 and = 5
=
[( 2 × 5) + (29 × 3) ]
= 15( 10 + 87) = 15 × 97 = 1455
Answer:
b.
Step-by-step explanation:
We have to look at sign changes in f(x) to determine the possible positive real roots.
There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.
Now we have to look at sign changes in f(-x) to determine the possible negative real roots.
There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:
1 positive
3 or 1 negative
We need to pair them up now with all the possible combinations.
If we have 1 positive and 1 negative, we have to have 2 imaginary
If we have 1 positive and 3 negative, we have to have 0 imaginary
Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.