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Firdavs [7]
3 years ago
6

given that a1=5 and a2=15 are the first two terms of a geometric sequence, determine the values of a3 and a10. Show the calculat

ions that lead to your answer​
Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
7 0

a_3 is 45 and a_10 is 98415

Step-by-step explanation:

Given

a_1 = 5

a_2 = 15

First of all we have to calculate the common ratio of the sequence. The common ratio is the ratio between two consecutive terms of a geometric sequence.

So,

r=\frac{a_2}{a_1} = \frac{15}{5} = 3

The explicit formula for geometric sequence is:

a_n = a_1.r^{n-1}

Putting the value of r and a_1

a_n = 5.(3)^{n-1}

Putting n=3 in the explicit formula

a_3 =5.3^{3-1}\\= 5 * 3^2\\=5 * 9\\= 45

Putting n=10 for tenth term

a_{10} =5.3^{10-1}\\=5*3^9\\=5 * 19683\\=98415

Hence,

a_3 is 45 and a_10 is 98415

Keywords: Geometric sequence, Explicit formula

Learn more about geometric sequence at:

  • brainly.com/question/10978510
  • brainly.com/question/11007026

#LearnwithBrainly

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Aquí, queremos saber la cantidad de autos que ingresarán al garaje cuando esté completamente ocupado.

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