Question

The third term of a g.P is 1/2 and second term is 16 find the g.P

Answer 1

Answer:

g.p. is .. 512,16,1\2............

Step-by-step explanation:

in atachment .....

Answer 2

Answer:

Concept:

The common ration between each term of the GP is 1/32. Hence the GP is 512, 16, 1/2.

Given:

The third term of a G.P = $\frac{1}{2}$

Second term of a G.P = 16

To Find:

G.P = ?

Solution:

Step 1:

Third term of G.P = $\frac{1}{2}$

$a_{3}$$=\frac{1}{2}$

Second term of G.P = 16

$a_{2}$=16

Step 2:

By Formula,

G.P can be written in form of = $a.ar,ar^{2},ar^{3},...$

G.P = $ar^{n-1}$

$a_{3} = ar^{3-1} = ar^{2}$

$ar^{2} = \frac{1}{2}$

$a_{2}$ $= ar^{2-1}$ $= ar$

$ar = 16$

Step 3:

By simplifying $ar^{2}$ and ar

∴ we get ,

r = $\frac{1}{2}$ ×$\frac{1}{16}$

r = $\frac{1}{32}$

Step 4:

Substitute r in ar,

a$(\frac{1}{32})=16$

$\frac{a}{32}$ = 16

a=512

Step 5:

Substitute a and r in G.P Formula

G.P = $a.ar,ar^{2},ar^{3},...$

G.P = 512 , 512 × $(\frac{1}{32})$ , 512 ×$(\frac{1}{32})^{2}$ , 512 × $(\frac{1}{32})^{3}$,...

by simplifying this we get,

G.P = 512 , 16 , $\frac{1}{2}$ ,..

Result:

G.P = 512 , 16 , $\frac{1}{2}$ ,...

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