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

Question

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

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Mathematics

1 answer:

Alekssandra [29.7K] · Answer 1 · 2022-02-25T23:43:24+03:00

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

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