Question

. If 1, a, b, c,16 are in G.P.(a, b, c are positive), then value of a+b+c is : 
16
14
12
8​

Answer 1

Answer:

16 is the correct answer

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

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

• 16

• 14

• 12

• 8

EVALUATION

Here it is given that 1, a, b, c , 16 are in G.P

Let common ratio = r

Since a, b, c are positive

So r is positive

5 th term = 16

$\sf{ \implies \: 1 \times {r}^{4} = 16 }$

$\sf{ \implies \: {r}^{4} = 16 }$

$\sf{ \implies \: {r}^{4} = {2}^{4} }$

$\sf{ \implies \: r = 2 }$

Thus we have

a = 1 × 2 = 2

b = 2 × 2 = 4

c = 4 × 2 = 8

Thus we have

a + b + c = 2 + 4 + 8 = 14

FINAL ANSWER

Hence the correct option is 14

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$If the middle term of a finite AP with 7 terms is 21 find the sum of all terms of the AP

https://brainly.in/question/30198388

2. find the 100th term of an AP whose nth term is 3n+1

https://brainly.in/question/22293445

3. 2,7,12,17,...sum of 12 terms of this A. P. is

https://brainly.in/question/24134044