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4 years ago

How to find nth term of a sequence in math?

Mathematics

1 answer:

worty [1.4K]4 years ago

7 0

Salutations!

To find the nth term, you will be needing a formula.

$a +(n-1) *d$

a stands for the first term (first number in the sequence)

d stands for the difference between two terms. (always remember to subtract from the 2nd term to the 1st term)

and the n is what we are going to find

so in your sequence: 5, 10, 15, 20

5 is a (as it is the first term)

d would be 5 ( 10 -5 =5)

$a+(n-1)*d$

$5+ (n-1) *5$

$5+5n-5$

$5n+0$

your nth term is $5n+0$

Hope this helps!

Have a great day!

You might be interested in

The sequence shown: 28, 22, 16, 10...)

noname [10]

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Step-by-step explanation:

Given sequence is:

28, 22, 16, 10

First of all, we have to determine if this is an arithmetic sequence or geometric sequence. for this purpose we will find the common difference.

Here

$a_1 = 28\\a_2 = 22\\a_3 = 16$

$d = a_2-a_1 = 22-28 =-6\\d = a_3-a_2 = 16-22 = -6$

As the common difference is same the sequence is an arithmetic sequence

Recursive Formula:

Recursive formula is the formula that uses the previous term and common difference to find the next term

As the common difference is -6

The recursive formula will be:

$a_n = a_{n-1} +(-6)\\a_n = a_{n-1} -6$

Explicit formula:

The explicit formula for an arithmetic sequence is:

$a_n = a_1+(n-1)d$

Putting the value of d and a_1

$a_n = 28 + (n-1)(-6)\\= 28 -6n+6\\= 34-6n$

35th term of the sequence:

To find the 35th term, putting n = 35

$a_{35} = 34-6(35)\\a_{35} = 34 - 210\\a_{35} = -176$

Sum:

$a_1 = 28\\a_{35} = -176$

The formula for sum of finite arithmetic sequence is:

$S_n = \frac{n}{2} (a_1+a_n)$

As we have to find sum of 35 terms, the formula will be:

$S_{35} = \frac{35}{2}(28-176)\\S_{35} = 17.5 (-148)\\=-2590$

Hence,

Recursive formula: $a_n = a_{n-1} -6$

Explicit Formula: $a_n = 34-6n$

35th term: -176

Sum of first 35 terms: -2590

Keywords: Arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

5 0

3 years ago

Which of the following can be constructed by drawing a line segment on paper and then folding the paper so that the endpoints of

TiliK225 [7]

I would say the answer is B

7 0

3 years ago

Read 2 more answers

Pls help. quickly please

AlekseyPX

Answer:

The Answer is B 2x+8=4

Step-by-step explanation:

I checked my answer in this app called QuickMath

5 0

3 years ago

Read 2 more answers

As students move to thinking about formulas it supports their conceptual knowledge of how the perimeter of rectangles can be put

kolezko [41]

Answer:

B. $P=l+w$

Step-by-step explanation:

Let l represent length of rectangle and w represent width of rectangle.

We have been given four formulas for the perimeter of rectangle. We are asked to choose the formula that displays a common student error for finding the perimeter.

We know that perimeter of a polygon is sum of all sides of the polygon. We also know that rectangle is polygon having two sets of equal sides.

The perimeter, P, of rectangle will be sum of its all sides that is:

$P=l+w+l+w$

Combine like terms:

$P=2l+2w$

Factor out 2:

$P=2(l+w)$

Upon looking at our given choices, we can see that formula represented by option B displays a common student error for finding the perimeter.

7 0

4 years ago

Quadrilateral A has side lengths 6, 9, 9, and 12. Quadrilateral B is a scaled copy of A with its shortest side of length 2. What

dsp73

Answer:

Step-by-step explanation:

If the Quadrilateral A has side lengths 6, 9, 9, and 12 respectively and Quadrilateral B is a scaled copy of A with its shortest side of length 2, then to determine the scale used, we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown;

ratio of shortest side

B:A = 2:6 = 1:3

This means that the quadrilateral B is 3 times smaller than A.

To find the perimeter of quadrilateral B, we will add all the side length of A and divide by 3 to get the perimeter of quadrilateral A by 3 as shown;

Perimeter of quadrilateral B = (Perimeter of quadrilateral A)/3

Perimeter of quadrilateral A = 6+9+9+12

Perimeter of quadrilateral A = 36

Perimeter of quadrilateral B = 36/3

Perimeter of quadrilateral B = 12

Hence the perimeter of quadrilateral B is 12

8 0

3 years ago