Pucusana
contestada

The first term of an arithmetic sequence is −12 . The common difference of the sequence is 7. What is the sum of the first 30 terms of the sequence? Enter your answer in the box.

Respuesta :

MathPhys

Answer:

2685

Step-by-step explanation:

The nth term of an arithmetic sequence is:

aₙ = a₁ + d (n − 1)

where a₁ is the first term and d is the common difference.

Here, a₁ = -12 and d = 7:

aₙ = -12 + 7 (n − 1)

aₙ = -12 + 7n − 7

aₙ = -19 + 7n

The sum of the first n terms of an arithmetic sequence is:

S = (n/2) (a₁ + aₙ)

First, we find the 30th term:

a₃₀ = -19 + 7(30)

a₃₀ = 191

Now we find the sum:

S = (30/2) (-12 + 191)

S = 2685

The sum provided by the the first 30 terms in the arithmetic sequence would be as follows:

[tex]2685[/tex]

Arithmetic Sequence

  • An arithmetic sequence is a set of integers that follow a specific pattern.
  • If you take any number in the sequence and divide it by the preceding one, and the result is always the same or constant, the sequence is an arithmetic sequence.

First term [tex](a)=-12[/tex]

Common difference [tex](d)=7[/tex]

Number of terms [tex](n)=30[/tex]

Sum of [tex]n[/tex] terms [tex]S_n=\frac{n}{2} [2a+(n-1)]d[/tex]

                                [tex]=\frac{30}{2}[2(-12)+(30-1)7][/tex]

                                [tex]=15(-24+203)\\=15(179)\\=\textbf{2685}[/tex]

Find out more information about "arithmetic sequence" here:

brainly.com/question/16130064

Otras preguntas