Question

The sum of an infinite G.P. $\frac{80}{9}$ and its common ratio is $\frac{-4}{5}$. Find its first term.

Answer 1

Hey dear,

● Answer-
a = 16

● Explaination-
# Given-
S∞ = 80/9
r = -4/5

# Solution-
Sum to infinity in geometric progression is approximated as-
S∞ = a / (1-r)
a = S∞ (1-r)
a = 80/9 (1+4/5)
a = 80/9 (9/5)
a = 80/5
a = 16

Therefore, first term in given geometric progression is 16.

Hope it helps you.
Keep asking...

Answer 2

$\textsf \green {Solution }$

$\textsf \red {If a , r are first term and }$
$\textsf \red { common ratio of infinite G.P}$

$\textsf \red {Sum of infinite G.P S= \frac{a}{1-r} } [tex]{ S=\frac{80}{9} }$
$\implies \Big (\frac{a}{\left ( {1-\frac{-4}{5}} \right )}\Big )=\frac{80}{9}$
$a = \frac{80}{9} \cdot \left (1-\frac{-4}{5} \right )$

$a = \frac {80}{9} \cdot \frac {(5 + 4)}{5}$

$=\frac{80×(9)}{9×5}$

=$ 16$

Therefore ,

a = $16$

•••••