Math, asked by priyanimmaluri303, 5 months ago

If the 5th and 10th term of a GP are 32 and 1024 respectively.find the 11th term of the GP

Answers

Answered by BrainlyPopularman
11

GIVEN :

• 5th term of G.P. = 32

• 10th term of G.P. = 1024

TO FIND :

11th term of G.P. = ?

SOLUTION :

• We know that nth term of G.P. –

  \\ \implies \large{ \boxed{\bf  T_n = a {r}^{n - 1}}}\\

• According to the first condition –

  \\ \implies\bf  T_5 =32 \\

  \\ \implies\bf  a {r}^{5- 1}=32 \\

  \\ \implies\bf  a {r}^{4}=32 \: \:  \:  \:  \:  \:   \:  \:  \:  \:  -  -  - eq.(1) \\

• According to the second condition –

  \\ \implies\bf  T_{10} =1024 \\

  \\ \implies\bf  a {r}^{10-1}=1024 \\

  \\ \implies\bf  a {r}^{9}=1024 \\

  \\ \implies\bf  (a {r}^{4})({r}^{5}) =1024 \\

• Using eq.(1) –

  \\ \implies\bf  (32)({r}^{5}) =1024 \\

  \\ \implies\bf {r}^{5} = \cancel\dfrac{1024 }{32}\\

  \\ \implies\bf {r}^{5} =32\\

  \\ \implies\bf {r}^{5} ={2}^{5} \\

  \\ \implies \large{ \boxed{\bf r = 2}} \\

• Put the value of 'r' in eq.(1) –

  \\ \implies\bf  a{(2)}^{4}=32\\

  \\ \implies\bf  a(16)=32\\

  \\ \implies\bf  a= \cancel \dfrac{32}{16}\\

  \\ \implies \large{ \boxed{\bf a=2}}\\

▪︎ 11th term of G.P. –

  \\ \implies\bf  T_{11} = (2){(2)}^{11- 1}\\

  \\ \implies\bf  T_{11} = (2){(2)}^{10}\\

  \\ \implies\bf  T_{11} = (2)(1024)\\

  \\ \implies \large{ \boxed{\bf  T_{11} = 2048}}\\

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