URGENT!!! plz help me with these two

Mathematics

1 answer:

Evgesh-ka [11]3 years ago

6 0

Answer:

hope that helps!!

Step-by-step explanation:

the first one is A

the second one is (2,-1)

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Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....

lina2011 [118]

Answer:Answer:

$\sum\left {{7} \atop {1}} \right -n(3+n)$

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as $S_n = \frac{n}{2}[2a+(n-1)d]$

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

$S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70$

The sum of the nth term of the sequence will be;

$S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)$

The sigma notation will be expressed as $\sum\left {{7} \atop {1}} \right -n(3+n)$ . <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>

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3 years ago

What is the 30th term of the arithmetic series 4, 7, 10, … ?

Irina18 [472]

$a_1=4;\ a_2=7;\ a_3=10\\\\d=a_2-a_1\to d=7-4=3\\\\a_n=a_1+(n-1)d\to a_n=4+(n-1)\cdot3=4+3n-3=3n+1\\\\\boxed{a_n=3n+1}\\\\a_{30}=3\cdot30+1=90+1=91\\\\Answer:\boxed{a_{30}=91}$