Math, asked by Chhavig1534, 9 months ago

Find the sum of the first 6 terms of 5,10,20

Answers

Answered by ramsuratawasthi79
1

Answer:

first 6 terms are 5,10,20,40,80,160

Therefore, sum = 5+10+20+40+80+160

= 315.

Answered by Rohith200422
3

Question:

Find the sum of the first 6 terms of

5, 10, 20,.....

To find:

\bigstar Sum \: of \: first \: 6 \: terms \: t_{6} = ?

Answer:

Sum \: of \: first \: 6 \: terms \: is \:   \underline{ \: \sf \pink{\bold{160}} \: } .

Step-by-step explanation:

5, 10, 20,........

The given consecutive terms are in G.P.

 \star First \: term \underline{ \: (a) = 5 \: }

 \star  Common\: ratio(r) = \frac{t _{2}}{t  _{1}}

  t _{2}  = 10

  t _{1}  = 5

\implies \frac{10} {5}

\implies \underline{ \: r = 2 \: }

 no.of\:terms\:\underline{\:n=6\:}

t _{n} =  a{r}^{n-1}

t _{6} =  a{r}^{5}

\implies 5{(2)}^{5}

\implies 5 × 32

\implies\boxed{t _{6} = 160}

\therefore  \underline{ \: Sum \: of \: first \: 6 \: terms \: is \:  \sf \pink{\bold{160}} \: }.

More information:

★ If three consecutive terms are in G.P.

= ac

★ General term of G.P.

a , ar , ar², ar³, ar⁴,.....

\bigstar  {n}^{th} \: term \: </u></strong><strong><u>= </u></strong><strong><u>t _{n} =  a{r}^{n-1} </u></strong><strong><u>

\bigstar no.of \: terms \:  \underline{ \: </u></strong><strong><u>t _{n} =  a{r}^{n-1} </u></strong><strong><u>\</u></strong><strong><u>:</u></strong><strong><u>}</u></strong><strong><u>

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