3 years ago

What is the 5th term of an arithmetic sequence if t2 = -5 and t6 = 7

Mathematics

1 answer:

RUDIKE [14]3 years ago

5 0

An=Asub1+d(n-1)
Asub5= -5+½(4)
=-5+7
=2

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Calculate the coefficient of x4y18 in the expansion of (x − y)22

Oksana_A [137]

Binomial theorem:

$(x-y)^n=\displaystyle\sum_{k=0}^n\binom nkx^k(-y)^{n-k}$

The term with $x^4y^{18}$ corresponds to $n=18+4=22$ and $k=4$ (or $k=18$ , since $\dbinom nk=\dbinom n{n-k}$ ).

So, the coefficient of this term is

$\dbinom{22}4(-1)^{18}=\dbinom{22}4=\dfrac{22!}{4!(22-4)!}=7315$