Question

If k ,2k-1 and 2k+1 are the three consecutive of ap find the value of k

Answer 1

AnsWer :

k = 5.

SolutioN :

Let's

• The three consecutive of AP be :
• a , b , c.

$\tt \dagger \: \: \: \: \: a = k .$

$\tt \dagger \: \: \: \: \: b = 2k - 1.$

$\tt \dagger \: \: \: \: \: c = 2k + 1.$

We have, Formula :

$\tt \dagger \: \: \: \: \: d = b - a$

$\tt \dagger \: \: \: \: \: d = c - b$

$\tt \dagger \: \: \: \: \: b = \dfrac{a + c}{2}$

$\tt : \implies 2(k - 1) = \dfrac{k + 2k + 1}{2}$

$\tt : \implies 2(2k - 2 )= k + 2k + 1$

$\tt : \implies 4k - 4= k + 2k + 1$

$\tt : \implies 4k - 4= 3k + 1.$

$\tt : \implies k= 1 + 4$

$\tt : \implies k= 5.$

Therefore, the value of k is 5.

$\rule{200}2$

Formula Use :

$\tt \dagger \: \: \: \: \: b = \dfrac{a + c}{2}$