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3 years ago

Fully factorise X^3 - 100

Mathematics

1 answer:

PIT_PIT [208]3 years ago

5 0

Answer:

(x-10)(x²+10x+100)

Step-by-step explanation:

Given the expression

X^3 - 100

This ca also be expressed as;

X^3 - 100 = X³ - 10³

a³-b³ = (a-b)(a²+b²+ab)

Substitute a = x and b = 10

X³ - 10³ = (x-10)(x²+10²+10x)

X³ - 10³ = (x-10)(x²+10x+100)

Hence the factored form is (x-10)(x²+10x+100)

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3 years ago

Please answer soon I need this answer very quickly for math. Thank you!

Kazeer [188]

a. First five terms: 9,13,17,21,25

b. Sum of first 25 terms = 1425

c. The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.

Further explanation:

Given

Formula of sequence

$a_n=4n+5$

1. First 5 terms:

For first 5 terms, we have to put n=1,2,...5,

So,

$For\ n=1\\a_1=4(1)+5\\=4+5\\=9\\For\ n=2\\a_2=4(2)+5\\=8+5\\=13\\For n=3\\a_3=4(3)+5\\=12+5\\=17\\For\ n=4\\a_4= 4(4)+5\\=16+5\\=21\\For\ n=5\\a_5=4(5)+5\\=20+5\\=25\\First\ 5\ terms\ are: 9,13,17,21,25$

2. Sum of first 25 terms:

For that we have to find 25th term first

$a_{25} = 4(25)+5\\=100+5\\=105$

The formula for sum is:

$S_n=\frac{n}{2}(a_1+a_n)}\\Putting\ the\ values\\S_n=\frac{25}{2}(9+105)\\=12.5(114)\\=1425$

3. Type of sequence

The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.

i.e.

$d=4$

Keywords: Arithmetic sequence, Sum of arithmetic sequence

Learn more about arithmetic sequence at:

#LearnwithBrainly

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3 years ago

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Answer:

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Step-by-step explanation:

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