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3 years ago

Find the nth term of this number sequence 1, 10, 19, 28, ... Pls help

Mathematics

2 answers:

dalvyx [7]3 years ago

8 0

Answer:

The nth term = 9n - 8.

Step-by-step explanation:

This is an Arithmetic Sequence with common difference d =

10 - 1 = 19 - 10 = 28 - 19 = 9.

The nth term an = a1 + (n - 1)d where a1 = the first term and d = the common difference.

So the nth term = 1 + (n - 1)9

= 1 + 9n - 9

= 9n - 8.

kherson [118]3 years ago

5 0

Answer:

9n - 8

Step-by-step explanation:

The sequence is arithmetic since the difference between consecutive terms is common

d = 10 - 1 = 19 - 10 = 28 - 19 = 9

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d = 9, thus

$a_{n}$ = 1 + 9(n - 1) = 1 + 9n - 9 = 9n - 8, hence

$a_{n}$ = 9n - 8

You might be interested in

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

Arithmetic Sequence

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

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2 years ago

How many groups of 1/2 day are in 1 week?

weqwewe [10]

There are 14 groups of days are in 1 week.

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2 years ago

Find - 4 - 2 1/2 expression on the number line by drawing an arrow

Tema [17]

Answer:

Step-by-step explanation:

4 0

3 years ago

Please help ill give brianleist answer!!!!

GaryK [48]

Answer:

i think its option ccc ydi aeg

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3 0

3 years ago

Read 2 more answers

The present age of father is thrice as old as the age of daughter 5 years ago. If 5 years hence ,the age of father will be twice

pav-90 [236]

Answer:

Hence the daughter's present age is 15 years

The fathers present age is 35 years

Step-by-step explanation:

Let the present age of daughter be x

Let the present age of father be y

5 years ago;

Daughter's age = x - 5

Fathers age = y - 5

If the present age of father is thrice as old as the age of daughter 5 years ago, then;

y - 5 = 3(x-5)

y - 5 = 3x-15

y = 3x - 10 .... 1

In 5 years time;

Daughters age = x + 5

Fathers age = y + 5

If the age of father will be twice the age of his daughter in 5 years time then;

y+5 = 2(x+5)

y+5 = 2x + 10

y = 2x + 5 .....2

Equate 1 and 2;

3x - 10 = 2x + 5

3x - 2x = 5 + 10

x = 15

Since y = 2x + 5

y = 2(15) + 5

y = 35

Hence the daughter's present age is 15 years

The fathers present age is 35 years

3 0

2 years ago