Question

Если знаменатель геометрической прогрессии равен 3, а пятый ее член равен 162, то первый член этой прогрессии равен

Answer 1

B1=b5/q^4
b1=162:81=2

Answer 2

$q=3 \\ bn=b1* q^{(n-1)} \\ \\ b5=b1* q^{4} \\ \\ 162=b1* 3^{4} \\ 162=b1*81 \\ b1=162:81 \\ \\ b1=2$

Answer 3

Solution for Finding the First Term of a Geometric Progression

To find the first term of a geometric progression when the common ratio is 3 and the fifth term is 162, we can use the formula for the nth term of a geometric progression:

The formula for the nth term of a geometric progression is: \[a_n = a_1 \times r^{(n-1)}\]

Where: - \(a_n\) = the nth term - \(a_1\) = the first term - \(r\) = the common ratio - \(n\) = the term number

Calculation

Using the given information: - Common ratio (\(r\)) = 3 - Fifth term (\(a_5\)) = 162

We can use the formula to find the first term (\(a_1\)):

\[a_5 = a_1 \times 3^{(5-1)}\]

Calculation Steps

\[162 = a_1 \times 3^4\] \[162 = a_1 \times 81\] \[a_1 = \frac{162}{81}\] \[a_1 = 2\]

Therefore, the first term of this geometric progression is 2.