What is the recursive formula for this geometric sequence 2, -10, 50, -250

Mathematics

2 answers:

BlackZzzverrR [31]3 years ago

6 0

Answer:

$a_k=-5\cdot a_{k-1}, \,\,\,k=1,2,...\,\,\,\mbox{and}\,\,\,a_0=2$

Step-by-step explanation:

The recursion is as follows:

$a_k=-5\cdot a_{k-1}, \,\,\,k=1,2,...\,\,\,\mbox{and}\,\,\,a_0=2$

and unrolling the first few examples:

$a_0=2\\a_1=-5\cdot 2 = -10\\a_2= -5\cdot (-10) = 50\\a_3 = (-5) \cdot 50 = -250$

geniusboy [140]3 years ago

3 0

Answer: C

Step-by-step explanation:

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What is the binomial expansion of (x + 2y)7?

borishaifa [10]

<h2>Thus, the required "option 4)" is correct.</h2>

Step-by-step explanation:

We find,

$(x+2y)^7$

To find, the binomial expansion of of $(x+2y)^7$ = ?

We know that,

$(x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n$

∴ $(x+2y)^7$

Here, n = 7, x = x and y = 2y

$(x+2y)^7$ = $^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7$ $=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7$