Question

What r the 1st 5 terms of the geometric progression with the 1st term 8 and the 6th term (-256)............( Plz be kind enough to send me the answer with steps...)

Answer 1

$\large \bold \red{ \underline{answer}} \\ \\ \implies \bold{first \: \: 5th \: \: term \: \: of \: \: gp \: } \\ \\ \implies \bold{t1 = a = 8} \\ \\ \implies \bold{t2 = ar = 8( - 2) = - 16} \\ \\ \implies \bold{t3 = a {r}^{2} = 8( - 2) {}^{2} = 32 } \\ \\ \implies \bold{t4 = a {r}^{3} = 8( - 2) {}^{3} = - 64 } \\ \\ \implies \bold{t5 = a {r}^{4} = 8( - 2) {}^{4} = 128 } \\ \\ \implies \bold \green{ \underline{explanation}} \\ \\ \implies \bold{ \underline{given}} \\ \\ \implies \bold{a \: = 8} \\ \\ \implies \bold{t6 = - 256} \\ \\ \implies \bold{ \underline{find \: \: value \: \: of \: \: first \: \: 5th \: \: term \: \: of \: \: gp}} \\ \\ \implies \bold{a {r}^{5} = - 256 } \\ \\ \implies \bold{8 {r}^{5} = - 256} \\ \\ \implies \bold{ {r}^{5} = - 32} \\ \\ \implies \bold{ {r}^{5} = - 2 {}^{5} } \\ \\ \implies \bold{r = - 2} \\ \\ \implies \bold \orange \therefore {t1 \: = \: a \: = 8} \\ \\ \implies \bold{t2 = ar \: = 8( - 2) = - 16} \\ \\ \implies \bold{t3 = ar {}^{2} = 8( - 2) {}^{2} = 32} \\ \\ \implies \bold{t4 \: = a {r}^{3} = 8( - 2) {}^{3} = - 64 } \\ \\ \implies \bold{t5 \: = ar {}^{4} = 8( - 2) {}^{4} = 128}$