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3 years ago

The pattern of numbers below is an arithmetic sequence:

Mathematics

2 answers:

oee [108]3 years ago

6 0

Answer:

Option C is correct

Step-by-step explanation:

The common difference is 10,

So, the function is f(n + 1) = f(n) + 10 , where f(1) = 14

The recursive function for the arithmetic sequence is given by:

.....[1]

where d is the common difference of the two consecutive terms.

Given the arithmetic sequence :

14, 24, 34, 44, 54, .......

First term f(1) = 14

Common difference(d) = 10

Since,

24 -14 = 10

34-24 = 10

44-34 = 10 and so on....

Substitute d = 4 in [1], we have;

Therefore, the recursive function used to generate the sequence is,

and f(1) = 10

Lerok [7]3 years ago

6 0

Answer:

C is indeed correct

Step-by-step explanation:

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cluponka [151]

Answer: They read for a equal amount of time.

Step-by-step explanation:

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Proof:

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3 years ago

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What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

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3 years ago