Mathematics : asked on ptrlvn01
 08.03.2022

Find the 64th term of an arithmetic sequence 29 38 47

. 23

Step-by-step answer

26.12.2022, solved by verified expert

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Mathematics
Step-by-step answer
P Answered by PhD

a_{n} = a_{1} + d(n - 1)  ; a₁ is the first term, d is the difference between terms, and n is the term

-4, -21, -38, ...   ⇒   a₁ = -4, d = -17

a_{n} = -4 - 17(n - 1)

   = -4 - 17n + 17

   = 13 - 17n

a_{64} = 13 - 17(64)

    = 13 - 1088

    = 1075

1075

Mathematics
Step-by-step answer
P Answered by Master

The 64th term of the arithmetic sequence is -1075.

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same.

The nth term of an arithmetic sequence is given by:

a_n = a_1 + (n-1)d

In which a_1 is the first term.

−4,−21,−38

First term -4, so a_1 = -4

Common difference of d = -38 - (-21) = -21 - (-4) = -17

Thus

a_n = a_1 + (n-1)d

a_n = -4 - 17(n-1)

Find the 64th term of the arithmetic sequence

This is a_{64}. So

a_n = -4 - 17(n-1)

a_{64} = -4 - 17(64-1) = -4 - 1071 = -1075

The 64th term of the arithmetic sequence is -1075.

Mathematics
Step-by-step answer
P Answered by PhD

a_{n} = a_{1} + d(n - 1)  ; a₁ is the first term, d is the difference between terms, and n is the term

-4, -21, -38, ...   ⇒   a₁ = -4, d = -17

a_{n} = -4 - 17(n - 1)

   = -4 - 17n + 17

   = 13 - 17n

a_{64} = 13 - 17(64)

    = 13 - 1088

    = 1075

1075

Mathematics
Step-by-step answer
P Answered by Specialist

a_{64}=917

Step-by-step explanation:

Given that,

The arithmetic sequence is :

-28,-13,2

First term = -28

Common difference = -13-(-28) = 15

We need to find the 64th term of the sequence. The nth term of the sequence is given by :

a_n=a+(n-1)d

Put all the values,

a_{64}=-28+(64-1)15\\\\=917

So, the 64th term of the sequence is equal to 917.

Mathematics
Step-by-step answer
P Answered by Specialist

-313

Step-by-step explanation:

a1=2; d=-5

a64=2-5(64-1)=-313

Mathematics
Step-by-step answer
P Answered by PhD

a_6_4=-313

Step-by-step explanation:

we know that

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant called the common difference

In this problem we have

2,-3,-8,...

Let

a_1=2\\a_2=-3\\a_3=-8

a_2-a_1=-3-(2)=-5\\a_3-a_2=-8-(-3)=-5

The common difference d is equal to -5

We can write an Arithmetic Sequence as a rule

a_n=a_1+d(n-1)

where

d is the common difference

a_1 is the first term

n is the number or terms

Find the 64th term

we have

a_1=2

d=-5

n=64

substitute

a_6_4=2+(-5)(64-1)

a_6_4=-313

Mathematics
Step-by-step answer
P Answered by Specialist

The 64th term of the arithmetic sequence is -1075.

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same.

The nth term of an arithmetic sequence is given by:

a_n = a_1 + (n-1)d

In which a_1 is the first term.

−4,−21,−38

First term -4, so a_1 = -4

Common difference of d = -38 - (-21) = -21 - (-4) = -17

Thus

a_n = a_1 + (n-1)d

a_n = -4 - 17(n-1)

Find the 64th term of the arithmetic sequence

This is a_{64}. So

a_n = -4 - 17(n-1)

a_{64} = -4 - 17(64-1) = -4 - 1071 = -1075

The 64th term of the arithmetic sequence is -1075.

Mathematics
Step-by-step answer
P Answered by Master

a_{64} = -313

Step-by-step explanation:a_{64} = 2 -135

This is the Arithmetic Sequence Formula->  a_{n} = a_{1} + (n+1) d

1) The d represents your difference of the equation. You can find it by finding a pattern between the three numbers given, which is -5

2) Now that we've found our difference, we can plug it into this lovely sequence we have a_{64} = a_{1} + (64-1) -5 (by the way, your n represents your term that you plug into the equation)

3) a_{64} = 2 + (64-1) -5  This also means that a_{1} is our first term, which is 2

4) Simplify a_{64} = 2 + (63) -5 --> a_{64} = 2 +-315

5) a_{64} = -313

The formula is confusing at first, but it becomes easier once your learn the patterns!

Mathematics
Step-by-step answer
P Answered by PhD

1071

Step-by-step explanation:

a(n) = a +(n-1)d

a=-4

d=-21+4=-17

°.° a(64) = -4 +(64–1)-17

             =-1071

hope this helps

Mathematics
Step-by-step answer
P Answered by PhD

197

Step-by-step explanation:

The nth term is 3n+5

so the 64th term will be

(3 x 64)+5

192+5

= 197

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