Verified answer

Answer:

Therefore, (2k-1)-(k+9) = (2k+7)-(2k-1)

2k-1-k-9 = 2k+7-2k+1

k-10 = 7+1

k=10+8

k= 18

Hence, if k=18, the consecutive terms k+9,2k-1 and 2k+7 are in AP.

[tex]k + 11 = a[/tex]

[tex]2k - 1 = c[/tex]

[tex]2k + 7 = b[/tex]

[tex]To \: be \: in \: A.P[/tex]

[tex]a + c = 2b \\ \\ k + 11 + 2k + 7 = 2(2k - 1) \\ \\ 3k + 18 = 4k - 2 \\ \\ 3k - 4k = - 2 - 18 \\ \\ - k = - 20 \\ \\ k = 20[/tex]