Question

Q.5 The sum of 3 terms of a GP is 21 and their product is 1 then the common ratio is.......
a) 1
b) 2
c) 4
d) 8​

Answer 1

It seems question has some mistakes. The correct question should be:

The sum of 3 terms of a GP is 21/4 and their product is 1 then the common ratio is...

Answer:

option c) 4 is correct.

Step-by-step explanation:

Given,

The sum of 3 terms of a GP is 21/4 and their product is 1.

To find : the common ratio

Solution:

Let the three terms be a/r , a , ar.

Then, Sum of terms = a/r + a + ar ...(i)

and, a/r * a * ar = 1

or, a³ = 1

or, a = 1

Substituing a = 1 in eq(i):

1/r + 1 + r = 21/4

or, 1 + r + r² = 21r / 4

or, 4 + 4r + 4r² = 21r

or, 4r² - 17r + 4 = 0

or, ( 4r - 1)(r - 4) = 0

i.e 4r - 1 = 0 or r - 4 = 0

i.e r = 1 / 4 or r = 4

Hence, Common ratio is 4.

Therefore, option c) 4 is correct.

Answer 2

Correct Question :- The sum of 3 terms of a GP is 21/4 and their product is 1 then the common ratio is ?

a) 1

b) 2

c) 4

d) 8

Solution :-

Let us assume that, the required 3 terms of GP are a/r, a and ar .

given that,

→ Product of three terms = 1

so,

→ (a/r) * a * ar = 1

→ a³ = 1

cube root both sides,

→ a = 1

also, given that,

→ sum of terms = 21/4

→ (a/r) + a + ar = 21/4

putting value of a , we get,

→ (1/r) + 1 + r = 21/4

→ (1 + r + r²)/r = 21/4

→ 4r² + 4r + 4 = 21r

→ 4r² - 17r + 4 = 0

→ 4r² - 16r - r + 4 = 0

→ 4r(r - 4) - 1(r - 4) = 0

→ (r - 4)(4r - 1) = 0

→ r = 4 or (1/4) .

therefore , from given options we can conclude that, the common ratio is 4. (C) (Ans.)

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