Question

for what values of k will be consecutive terms 2K+1, 3K and 5k + 1 form an AP.​

Answer 1

$\sf if \: three \: consecutive \: terms \: \red{a,b,c} \: forms \:AP$

$\sf \purple{then}$

$\blue{ \boxed{ \sf 2b = a + c}}$

$\sf \purple{here}$

• $\sf a =2 k + 1$
• $\sf b = 3k$
• $\sf c = 5k + 1$

$\implies \sf 2(3k) = (2k + 1) + (5k + 1)$

$\implies \sf 6k = 7k + 2$

$\implies \sf 7k - 6k = - 2$

$\orange{ \therefore \sf k = - 2}$

HOPE IT HELPS!!