Answer:To determine the value of kk in the given arithmetic progression (A.P.), we need to use the property that consecutive terms in an A.P. have a common difference.The common difference (dd) between consecutive terms is the difference between any two consecutive terms.Given three consecutive terms:k+2k+24k−64k−63k−23k−2To find the common difference, we subtract the second term from the first and the third term from the second:(4k−6)−(k+2)=4k−6−k−2=4k−k−6−2=3k−8(4k−6)−(k+2)=4k−6−k−2=4k−k−6−2=3k−8(3k−2)−(4k−6)=3k−2−4k+6=3k−4k−2+6=−k+4(3k−2)−(4k−6)=3k−2−4k+6=3k−4k−2+6=−k+4Since these differences must be equal, we have:3k−8=−k+43k−8=−k+4Now, let's solve for kk:3k−8=−k+43k+k=8+44k=12k=124k=33k−83k+k4kkk=−k+4=8+4=12=412=3So, the value of kk is d. 3
d. 3.
Step-by-step explanation:
