Question

Question :-

lf the First two consecutive terms of a G.P are 125 & 25,
Then find the 6th term.

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Answer 1

Step-by-step explanation:

$\large\bold\red{Question →}$

★ lf the First two consecutive terms of a G.P are 125 & 25, Then find the 6th term.

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$\large\bold\red{Answer →}$

★ Given :-

• First two consecutive terms of G.P are = 125 & 25

★ To Find :-

• The 6 term of given G.P

$\large\underline \bold \pink{Solution \: \mapsto}$

★ Clearly :-

• First term A = 125
• Second term AR = 25

★ Now,

⠀$∴ \bold \red{Common \: Ratio} \large\bold{ \: = \frac{AR}{A} } \\ \\ \large \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{25}{125} } \\ \\ \large \bold \pink{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: R = \frac {1}{5} }$

★ Therefore,

⠀⠀⠀⠀$\mapsto \: \large \bold {6 \: term \: of \: G.P } \large \bold \pink{ = {ar}^{5} } \\ \\ \large \bold { = 125 \times \ (\frac{1}{5} ) {}^{5} } \\ \\ \large \bold{ = \frac{125}{3125} } \\ \\ \large \bold \red{ = \frac{1}{25} }$

★ Hence,

• The 6 term = $\large\bold\pink{\frac{1}{25}}$

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$\large\colorbox{pink}{Hope lt'z Help You ❥ }$

Answer 2

$\huge\boxed{\fcolorbox{red}{blue}{Answer}}$

First term A = 125

Second term AR = 25

Common ratio -

$\frac{ar }{a}$

$\frac{25}{125}$

R= $\frac{1}{5}$

$6termofG.P=ar5=125× (1/5)⁵=125/3125=1/25</p><p>$

Thus 6 term is $\frac{1}{5}$