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Find the 8th term of the geometric sequence 7,28,112

Sagot :

mhanifa

Answer:

  • 7*4⁷ or 114688

Step-by-step explanation:

This is a GP with:

  • The first term of a₁ = 7
  • Common ratio r = 4

Use the nth term formula:

  • aₙ = a₁rⁿ⁻¹
  • a₈ = 7*4⁷ = 114688
semsee45

Answer:

114688

Step-by-step explanation:

General form of a geometric sequence:

  [tex]a_n=ar^{n-1}[/tex]

where:

  • [tex]a_n[/tex] is the nth term
  • a is the first term
  • r is the common ratio

Given sequence:  7, 28, 112, ...

First term

From inspection of the given sequence, the first term is 7:

[tex]\implies a=7[/tex]

Common ratio

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{28}{7}=4[/tex]

Equation for the nth term

Substitute the found values of a and r into the formula to create an equation for the nth term:

[tex]\implies a_n=7(4)^{n-1}[/tex]

8th term

To find the 8th term, substitute n = 8 into the found equation:

[tex]\implies a_8=7(4)^{8-1}[/tex]

[tex]\implies a_8=7(4)^7[/tex]

[tex]\implies a_8=7(16384)[/tex]

[tex]\implies a_8=114688[/tex]

Learn more about geometric sequences here:

https://brainly.com/question/27783194

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