Question

Find the 64th term of the arithmetic sequence 2, -3, -8, ...2,−3,−8,...

Answer 1

The 64th term of the arithmetic sequence is found using the formula for the n-th term of an arithmetic sequence. With a common difference of -5, the 64th term is calculated to be -313.

Step-by-step explanation:

To find the 64th term of the arithmetic sequence given by 2, -3, -8, ..., we first need to identify the common difference of the sequence.

The common difference (d) is found by subtracting the first term from the second term:

d = -3 - 2 = -5

Now, we can use the formula for the n-th term of an arithmetic sequence, which is an = a1 + (n - 1)d.

For the 64th term (a64):

a64 = 2 + (64 - 1)(-5) = 2 + (63)(-5)

a64 = 2 - 315 = -313

Therefore, the 64th term of the sequence is -313.

Answer 2

`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`