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aniked [119]
2 years ago
15

Need help now!! 20 points!!

Mathematics
1 answer:
Gelneren [198K]2 years ago
3 0

When you have something like this, all you need to do is substitute the values, the last is for what value of x

For the first one;

((x^2+1)+(x-2))(2)

(x^2+x-1)(2)

(2)^2+(2)-1

4+2-1

5

For the second one;

((x^2+1)-(x-2))(3)

(x^2-x+3)(3)

(3)^2-(3)+3

9-3+3

9

For the last one;

3(x^2+1)(7)+2(x-2)(3)

3((7)^2+7)+2((3)-2)

3(49+7)+2(3-2)

3(56)+2(1)

168+2

170

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The third term of the sequence is 120. The fifth term is 76.8 The explicit rule for the geometric sequence is an=?(?)n-1
gulaghasi [49]

Answer:

The explicit rule of the geometric sequence

 aₙ   = 187.5 (0.8)ⁿ⁻¹

Step-by-step explanation:

<u><em> Step(i):-</em></u>

Given that the third term of the sequence = 120

        tₙ = a rⁿ⁻¹  

       t₃  = a r³⁻¹ = ar²

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Given that the fifth term of the given geometric sequence = 76.8

        tₙ = a rⁿ⁻¹  

       t₅  = a r⁵⁻¹ = a r⁴

   76.8  = a r⁴...(ii)

<u><em>Step(ii):</em></u>-

 Dividing (ii) and (i)

         \frac{ar^{4} }{ar^{2} } = \frac{76.8}{120}

        r²   = 0.64

       r    =√ 0.64 = 0.8

Substitute r= 0.8 in equation (i)

         120 = ar²

       120 = a(0.8)²

⇒      a = \frac{120}{0.64} =187.5

<u><em>Step(iii):-</em></u>

The explicit rule of the geometric sequence

                 aₙ  = a rⁿ⁻¹

put a= 187.5  and r = 0.8

                aₙ   = 187.5 (0.8)ⁿ⁻¹

 

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