Question

if k+1,3k and 4k+2 be any 3 consecutive terms of an ap find the value of k​

Answer 1

Answer:

$\boxed{\text{\bf k = 3}}$

Step-by-step explanation:

$\text{In an AP,the difference between any two consecutive terms is same} \\\\ \text{given consecutive terms,} \\ k+1,3k,4k+2 \\\\ => common \ difference = 3k-(k+1) = (4k+2)-3k \\\\ 3k-k-1=4k+2-3k \\\\ 2k-1=k+2 \\\\ 2k-k=2+1 \\\\\boxed{\bf k=3}$

Answer 2

Step-by-step explanation:

If k+1, 3k and 4k+2 are the consecutive terms of an AP:

Taking common difference equal:

a2-a1=a3-a2.

3k-(k+1)=4k+2-3k

3k-k-1=k+2

2k-k=2+1

k=3.