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3 years ago

Find the sum of a finite arithmetic sequence from n = 1 to n = 10, using the expression 3n − 8.

Mathematics

1 answer:

maw [93]3 years ago

8 0

Answer:

The answer is 85

Step-by-step explanation:

The equation used to find the sum of an arithmetic series is: (n/2) * (a1 + an).

n in this case is 10 (the number of numbers in the series)

an is 22 (plug in 10 to the expression 3n-8)

and a1 is -5 (plug in 1 to the expression 3n-8)

so when you plug everything in to the final equation, you get

(10/2) * (-5 + 22)

5 * 17

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2 years ago

Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression −4(6)n − 1.

Verizon [17]

Answer:

Step-by-step explanation:

The formula of a sum of terms of a gometric sequence:

$S_n=a_1\cdot\dfrac{1-r^n}{1-r}$

a₁ - first term

r - common ratio

We have

$a_n=-4(6)^{n-1}$

Calculate a₁. Put n = 1:

$a_1=-4(6)^{1-1}=-4(6)^0=-4(1)=-4$

Calculate the common ratio:

$r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=-4(6)^{n+1-1}=-4(6)^n\\\\r=\dfrac{-4(6)^n}{-4(6)^{n-1}}=6^n:6^{n-1}\\\\\text{use}\ a^n:a^m=a^{n-m}\\\\r=6^{n-(n-1)}=6^{n-n+1}=6^1=6$

$\text{Substitute}\ a_1=-4,\ n=7,\ r=6:\\\\S_7=-4\cdot\dfrac{1-6^7}{1-6}=-4\cdot\dfrac{1-279936}{-5}=-4\cdot\dfrac{-279935}{-5}=(-4)(55987)\\\\S_7=-223948$

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3 years ago