Question

☆If 1, a, b, c,16 are in G.P.(a, b, c are positive), then value of a+b+c is : 

(i) 16

(ii) 14

(iii) 12

(iv) 8

please answer it fast ​

Answer 1

Given :- If 1, a, b, c,16 are in G.P.(a, b, c are positive), then value of a+b+c is : 

(i) 16

(ii) 14

(iii) 12

(iv) 8

Solution :-

Let us assume that, the first term of given GP series is a and common ratio is r .

so,

→ First term = a = 1 ------ Eqn.(1)

→ Second term = ar = a

→ Third term = ar² = b

→ Fourth term = ar³ = c

→ Fifth term = ar⁴ = 16 ------- Eqn.(2)

putting value of Eqn.(1) in Eqn.(2),

→ 1 * r⁴ = 16

→ r⁴ = 16

→ r⁴ = (±2)⁴

→ r = ± 2

since we have given that, a, b, c are positive , therefore, r is equal to 2 .

hence,

→ (a + b + c) = ar + ar² + ar³

→ (a + b + c) = 1*2 + 1*2² + 1*2³

→ (a + b + c) = 2 + 4 + 8

→ (a + b + c) = 14 (ii) (Ans.)

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Answer 2

Answer:

II) 14 and Happy Independence Day