Question

Pls help me solve the problem

Answer 1

Answer:

The 54th term is -855

Step-by-step explanation:

Since the sequence is arithmetic, then we have to use the rule of the nth term

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

a is the first term

d is the common difference

n is the position

The given sequence is -7, -23, -39

a=-7

d=-23-(-7)=-23+6=-16

We need to find the 54th term

n=54

Substitute them in the rule

$a_{54}=-7+(54-10)(-16)$

Solve it:

$a_{54}=-7+(53)(-16)\\ a_{54}=-7-848\\ a_{54}=-855$

The 54th term is -855

Answer 2

Answer:

The characteristic of an arithmetic sequence is:

• The difference between the consecutive terms is constant.

This difference between consecutive terms is called common difference and is denoted by (d)

STEP I

(finding the common difference)

As stated above, the common difference is the difference between consecutive terms and, thus, will be found out by subtracting any two consecutive terms.

-7 and -23 are two consecutive terms in the sequence!

Subtracting (-7) from (-23):

$\implies \mathsf{d = - 23 - ( - 7)}$

$\implies \mathsf{d = - 23 + 7}$

$\implies \mathsf{ \underline{d = -16}}$

STEP II

(Finding the nth term)

The formula used for finding the nth term of an arithmetic sequence is:

$\boxed{ \mathsf{a _{n} = a + (n - 1)d }}$

Here,

• $a_n$ = nth term
• a = first term
• d = common difference

The question asks us to find the 54th term of the sequence.

Substituting 54 for n:

$\implies \mathsf{a _{54} = a + (54 - 1)d }$

• The first term of the sequence is -7

substituting -7 for a and -16 for d

$\implies \mathsf{a _{54} = - 7+ (54 - 1)( - 16)}$

$\implies \mathsf{a _{54} = - 7+ (53)( - 16)}$

$\implies \mathsf{a _{54} = - 7 - 848}$

$\implies \mathsf{ \underline{a _{54} = - 855}}$

ANSWER:

The 54th term of the sequence is -855.

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Learn more about nth term of an AP here:

brainly.com/question/16613594

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Hope this helps!