Question

Find the 10th term of the geometric sequence 3, 15, 75, ...

Answer 1

hey mate here is ur answer

a=3

r=15/3=5.

t10=ar^(n-1)=ar⁹

t10=3×5⁹=5,859,375

hope it helps.

☆☆☆

Answer 2

10th term of the geometric sequence 3 , 15 , 75, . . . = 5859375

Given :

The geometric sequence 3 , 15 , 75, . . .

To find :

10th term of the geometric sequence 3 , 15 , 75, . . .

Concept :

For a geometric progression (GP)

$\displaystyle \sf{ }nth \: term \: of \: the \: GP = a \times {r}^{n - 1}$

Where , first term = a and common ratio = r

Solution :

Step 1 of 2 :

Find first term and common ratio

Here the given geometric sequence is 3 , 15 , 75, . . .

First term = a = 3

Common ratio = r = 15/3 = 5

Step 2 of 2 :

Calculate 10th term of the geometric sequence

10th term of the geometric sequence

$\displaystyle \sf{ = a \times {r}^{10 - 1} }$

$\displaystyle \sf{ = a \times {r}^{9} }$

$\displaystyle \sf{ = 3 \times {5}^{9} }$

$\displaystyle \sf{ = 3 \times 1953125 }$

$\displaystyle \sf{ = 5859375 }$

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