Question

The seventh term of a gp is eight times the fourth term. Find the 1st term if 5th term is 48.

Answer 1

$\huge{\mathfrak{\blue{\underline{Answer}}}}$

✝ According to the quesion :

$8(ab {}^{7 - 1} ) = ab {}^{4 - 1} \\ 8(ab {}^{6} ) =( ab {}^{ {}^{3} } ) \\ \\ 8( \frac{ab {}^{6} }{ab {}^{3} } ) = 1 \\ 8(b {}^{3} ) = 1 \\ b {}^{3} = \frac{1}{8} \\ b = \sqrt[3]{ \frac{1}{8} }$

✝ Common Ratio :

$\large{\implies{\blue{b=1/2}}}$

Given that the 5th term is 48

Hence ,

$ab {}^{5 - 1} = 48 \\ a( \frac{1}{2} ) {}^{4} = 48 \\ a( \frac{1}{16} ) = 48 \\ a (first \: term) = 16 \times 48$

$\huge{\implies{\mathcal{\blue{\underline{first\:term=768}}}}}$

✝ Note :

In a GP we can find the terms by using the formula :

$= ab {}^{n - 1}$

Where

a=First term

b=common ratio

n=number of terms