Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.

Given, ⇒ a + a 2 = -4 ⇒ a + ar = -4 ⇒ a(1 + r) = -4 ........(i) ⇒ a 5 = 4a 3 ⇒ ar 4 = 4ar 2 ⇒ r 2 = 4 ⇒ r = ± 2 Let r = 2. Substituting value of r in (i) we get, ⇒ a(1 + 2) = -4 ⇒ 3a = -4 ⇒ a = . G.P. = a, ar, ar 2 , ........ = ........ Let r = -2. Substituting value of r in (i) we get, ⇒ a(1 + (-2)) = -4 ⇒ -a = -4 ⇒ a = 4. G.P. = a, ar, ar 2 , ........ = 4, -8, 16, -32,........ Hence, G.P. = ........ or 4, -8, 16, -32.

The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

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-1, k and -1 are three consecutive terms of a G.P., then
(i) k = 1
(ii) k = -1
Which of the following is valid ?
only 1
only 2
both 1 and 2
either 1 or -1

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x + 9, 10 and 4 are in G.P. The value of x is :
16
8
-16
0

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Mathematics

Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.

GP

Related Questions

The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

-1, k and -1 are three consecutive terms of a G.P., then
(i) k = 1
(ii) k = -1
Which of the following is valid ?
only 1
only 2
both 1 and 2
either 1 or -1

x + 9, 10 and 4 are in G.P. The value of x is :
16
8
-16
0

Mathematics

Find a G.P. for which the sum of first two terms is -4 and the fifth term is 4 times the third term.

GP

Related Questions

The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.

-1, k and -1 are three consecutive terms of a G.P., then(i) k = 1(ii) k = -1Which of the following is valid ?only 1only 2both 1 and 2either 1 or -1

x + 9, 10 and 4 are in G.P. The value of x is :168-160

The first two terms of a G.P. are 125 and 25 respectively. Find the 5^th and the 6^th terms of the G.P.

-1, k and -1 are three consecutive terms of a G.P., then
(i) k = 1
(ii) k = -1
Which of the following is valid ?
only 1
only 2
both 1 and 2
either 1 or -1

x + 9, 10 and 4 are in G.P. The value of x is :
16
8
-16
0