The sum of the first two terms of a G.P. is −4 and the fifth term is 4 times the third term. Then, the first term of the G.P. is : 1. or 4 2. or 3. or 4. or 4

Question

KnowledgeBoat · Accepted Answer

Let the first term be a and the common ratio be r. Given, Sum of the first two terms is -4 ⇒ a + ar = -4 ⇒ a(1 + r) = -4 .....(1) Given, The fifth term is 4 times the third term. ⇒ ar5 - 1 = 4ar3-1 ⇒ ar4 = 4ar2 ⇒ r2 = 4 ⇒ r = ⇒ r = 2 or r = -2 Substituting r = 2 into equation 1 : ⇒ a(1 + 2) = -4 ⇒ 3a = -4 ⇒ a = . Substituting r = -2 into equation 1: ⇒ a[1 + (-2)] = -4 ⇒ a(1 - 2) = -4 ⇒ a(-1) = -4 ⇒ a = 4. Hence, option 4 is the correct option.

Mathematics

The sum of the first two terms of a G.P. is −4 and the fifth term is 4 times the third term. Then, the first term of the G.P. is : 1. or 4 2. or 3. or 4. or 4

G.P.

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Mathematics

The sum of the first two terms of a G.P. is −4 and the fifth term is 4 times the third term. Then, the first term of the G.P. is : 1. or 4 2. or 3. or 4. or 4

G.P.

Related Questions

How many terms of the G.P. 1, 4, 16, 64, …….. will make the sum 5461?6978

The sum of 7 terms of the G.P. 3, 6, 12, ………. is :181241381421

How many terms of the G.P. 1, 4, 16, 64, …….. will make the sum 5461?
6
9
7
8

The sum of 7 terms of the G.P. 3, 6, 12, ………. is :
181
241
381
421