which of the following word GP there GP write three more terms for 5, 55, 555
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ankitgupta82
Secondary School Math 10+5 pts
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, .....
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