3. Determine k so that k2 +4k+8,2k2 + 3k6 and 3k2 + 4k + 4 are three c

1.	3. Determine k so that k2 +4k+8,2k2 + 3k6 and 3k2 + 4k + 4 are three consecutiveterms of an A.P.
Answer» It is given that (3k− 2),(4k− 6) and(k+ 2) are three consecutive terms of an AP. ∴(4k− 6)−(3k− 2) =(k+ 2)−(4k− 6) ⇒ 4k− 6− 3k+ 2 =k+ 2− 4k+ 6 ⇒k− 4 =−3k+ 8 ⇒k+ 3k=8 + 4 ⇒ 4k=12 ⇒k=3 Hence, the value ofkis 3.

3. Determine k so that k2 +4k+8,2k2 + 3k6 and 3k2 + 4k + 4 are three consecutiveterms of an A.P.

Answer»

It is given that (3k− 2),(4k− 6) and(k+ 2) are three consecutive terms of an AP.

∴(4k− 6)−(3k− 2) =(k+ 2)−(4k− 6)

⇒ 4k− 6− 3k+ 2 =k+ 2− 4k+ 6

⇒k− 4 =−3k+ 8

⇒k+ 3k=8 + 4

⇒ 4k=12

⇒k=3

Hence, the value ofkis 3.