Question

show that a1,a2,......an form an AP where A is defined as an=9-5n

Answer 1

Hey !!!
Here is your answer !!

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Taking the value of n as 1 , 2 , 3 , 4 and so on

▶ a1 = 9 - 5 = 4 [ 9 - 5 × 1 ]

▶ a2 = 9 - 10 = - 1 [ 9 - 5 × 2 ]

▶a3 = 9 - 15 = - 6 [ 9 - 5 × 3 ]-

▶ a4 = 9 - 20 = - 11 [ 9 - 5 × 4 ]

now we can see that

a2 - a2 = - 1 - 4 = -5

a3 - a2 = - 6 + 1 = - 5

a4 - a3 = - 11 + 6 = - 5

a2 - a1 = a3 - a2 = a4 - a3
Hence common difference (d) is same


hence it is in AP !!

Proved ✔

Hope it helps :)