Question

for what values of k are 2k,5k +2,and 20k-4 consesecutive terms of GP??
PLEASE SOLVE??

Answer 1

Here is the required answer bro

Answer 2

2k,5k +2,and 20k-4 are in GP when k = 2 or k = -2/15.

Given:

2k,5k +2,and 20k-4 are in geometric progression.

To Find:

The value of k.

Solution:

Geometric progression is a special type of progression in which the consecutive terms bear a constant coefficient called a common ration, usually denoted by r.

Terms of a geometric progression are denoted by a, ar , ar², ar³,....a$r^{n-1}$

,..., where a is the first term. For 2k,5k +2, and 20k-4 to be in geometric progression it should satisfy :

For 2k,5k +2,and 20k-4 to be in geometric progression it should satisfy :

$\frac{5k +2}{2k}$ = $\frac{20k-4}{ 5k +2}$

⇒ (5k+2)² = (20k-4)(2k)

⇒ 25k² + 20k +4 = 40k² - 8k

⇒ 15k² -28k - 4 = 0

⇒ 15k²- 30k + 2k - 4 = 0

⇒ (k-2)(15k+2) = 0

⇒ k = 2 or k = -2/15

∴ 2k,5k +2,and 20k-4 are in GP when k = 2 or k = -2/15.

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