Question

for what valuevof k will k+9,2k-1 ad 2k+7 are the consecutive terms of an a.p.

Answer 1

Heya !!!



AP = K + 9 , 2K -1 and 2K+7.


Here,



T1 = K +9


T2 = 2K-1


And,


T3 = 2K+7

First term (T1) = K +9


And,


Common difference (D) = T2-T1



=> 2K -1 - (K +9)


=> 2K -1 - K -9


=> K -10


ALSO,



Common Difference (D) = T3-T2

=> 2K +7 - (2K -1)

=> 2K +7 - 2K +1

=> 8



As we know that,


Common difference of an AP is always Equal.



So,




T2-T1 = T3-T2



K -10 = 8


K = 8+10


K = 18.


HOPE IT WILL HELP YOU...... :-)

Answer 2

Hey!

Given AP :- ( k + 9 ) , ( 2k - 1 ) , ( 2k + 7 )

• When three nos. are the consecutive terms of an AP then , the middle term is equal to the mean of 1st and 3rd Term

Eg. :- AP as a , b , c

then ,
$\frac{a + c}{2} = b$


So,

$\frac{(k + 9) + (2k + 7)}{2} = 2k - 1$


3k + 16 = 4k - 2

3k - 4k = - 2 - 16

- k = - 18

k = 18 !!


So, k = 18 ...