The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

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Solution

Use your definitions:
the fifth term of a g.p. is 81 ---> $a r^{4} = 81$
second term is 24 -----> ar = 24

divide them:
$\frac{a r^{4}}{a r}$ = $\frac{81}{24}$

$r^{3}$ = $\frac{27}{8}$
r = $\frac{3}{2}$

then in ar=24
(3/2)a = 24
a = 16

the GP is
16, 24, 36, 54, 81, ...

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The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

Use your definitions: the fifth term of a g.p. is 81 ---> ar4=81 second term is 24 -----> ar = 24 divide them: ar4ar = 8124 r3 =278 r = 32 then in ar=24 (3/2)a = 24 a = 16 the GP is 16, 24, 36, 54, 81, ...

Use your definitions:
the fifth term of a g.p. is 81 ---> $a r^{4} = 81$
second term is 24 -----> ar = 24

divide them:
$\frac{a r^{4}}{a r}$ = $\frac{81}{24}$

$r^{3}$ = $\frac{27}{8}$
r = $\frac{3}{2}$

then in ar=24
(3/2)a = 24
a = 16

the GP is
16, 24, 36, 54, 81, ...