Question

Which of the following are GP? If they are GP. Write three more terms?
(i) 4, 8, 16 ..... (ii)1/3, −1/6, 1/12, .....
(iii) 5, 55, 555, .... (iv) −2, −6, −18 .....
(v) 1/2, 1/4, 1/6, ..... (vi) 3, −3², 3³, .....
(vii) x, 1, 1/x, ..... (viii) 1/√2, −2, 8/√2, .....
(ix) 0.4, 0.04, 0.004, .....

Answer 1

The Geometric Progression is given as

$a,ar,ar^{2},ar^{3} ,ar^{4},............,ar^{n-1},ar^{n}$

The term can said to be

$a_{1},a_{2}, a_{3}, a_{4},......., a_{n-1},a_{n}$

Where,$a_{n} = ar^{n-1}$

and sum is given as $a\frac{r^{n-1}-1 }{r-1}$

(i) 4, 8, 16 .....

a=4, r=2

So,next three terms are   $4*2^{3},4*2^{4} ,*4*2^{5}$

Which is 32,64,128

(ii)1/3, −1/6, 1/12, .....  

a= 1/3 and r is not given as mentioned, hence not in GP

(iii) 5, 55, 555, ....

a=5 and  r is not given as mentioned, hence not in GP

(iv) −2, −6, −18 .....

a=-2 and r=3

So,next three terms are   $-2*3^{3},-2*3^{4} ,-2*3^{5}$

Which is -54,-162,-486

(v) 1/2, 1/4, 1/6, .....

a=1/2 and  r is not given as mentioned, hence not in GP

(vi) 3, −3², 3³, .....

 a=3 and  r is not given as mentioned, hence not in GP

Thanks

Hope it helps

Answer 2

Answer:

x, 1,1/x...... Find 3 more terms