Question

If the numbers (5n+ 3), (4n+ 2) and (n-3) are in AP, then find the value of n.​

Answer 1

Answer:

-2

Step-by-step explanation:

since (5n+ 3), (4n+ 2) and (n-3) are in A.P

(4n+ 2) - (5n+ 3) = (n-3) - (4n+ 2)

⇒ 4n + 2 - 5n - 3 = n - 4n -3 -2

⇒ -n - 1 = -3n - 5

⇒ n+1 = 3n+5

⇒ 2n = -4

⇒ n = -2

VERIFICATION:

substitute '-2' in place of n

⇒ [5(-2) + 3]; [4(-2) + 2]; (-2 - 3)

⇒ -7, -6, -5

these are in A.P with common difference '+1'

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ALTERNATE PROCESS:

since (5n+ 3), (4n+ 2) and (n-3) are in A.P

(4n+ 2) = [(5n+ 3) + (n-3)]/2

⇒ 8n + 4 = 6n

⇒ 2n = -4

⇒ n = -2