Question

Find the first term of Gp.whose fifth term is 243 and common ratio is 3.​

Answer 1

Given :

• Fifth term of a Geometric progression is 243
• Common ratio of the progression is 3

To find :

• The First of the geometric progression

Solution :

Let the first term of the geometric progression be 'a'

The general terms of a geometric progression are ,

a , ar , ar² , ar³ , ar⁴ , ar⁵ , ar⁶ ,..........., a$\sf{r^{n-1}}$

Here ,

• First term = a
• Second term = ar
• Third term = ar²
• Fourth term = ar³
• Fifth term = ar⁴
• :
• :
• :
• :
• $\sf{n^{th}}$term = a$\sf{r^{n-1}}$

Where ,

• r is common ratio

• a is First term

We have ,

• r = 3 [ Common ratio

• ar⁴ = 243 [Fifth term]

By substituting the values we have ,

$: \implies \sf \: a {r}^{4} = 243 \\ \\ \\ : \implies \sf \: a(3) {}^{4} = 243 \\ \\ \\ : \implies \sf \: a(81) = 243 \\ \\ \\ : \implies \sf \: a = \frac{243}{81} \\ \\ \\ : \implies \boxed{\underline{\bf {\: a = 3}}}$

Hence , The First term of the given geometric progression is 3.

Answer 2

Explanation:

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