Question

What are the first three terms of a geometric sequence in which as = 25 and the common ratio is 5?
1 1
1
25'5
25,125,625
1 1 1
25'125 '625
O 125, 25, 5
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Answer 1

Answer:

The first three terms are: 25, 125 and 625

Step-by-step explanation:

Given

$a =25; r = 5$

Required

The first three terms

The nth term of a geometry progression is:

$T_n =ar^{n-1$

So, we have:

First term: $n = 1$

$T_n =ar^{n-1$

$T_1 =25 * 5^{1-1$

$T_1 =25 * 5^0$

$T_1 =25 * 1$

$T_1 =25$

Second term: $n = 2$

$T_n =ar^{n-1$

$T_2 =25 * 5^{2-1$

$T_2 =25 * 5^{1$

$T_2 =25 * 5$

$T_2 =125$

Third term: $n = 3$

$T_n =ar^{n-1$

$T_3 =25 * 5^{3-1$

$T_3 =25 * 5^{2$

$T_3 =25 * 25$

$T_3 =625$