Question

Show that the sequence defined by $a_{n}=5_{n}-7$ is an A.P., find its common difference

Answer 1

Answer:

Common difference = 5  and the given sequence is an A.P.

Step-by-step explanation:

Given :

an = 5n - 7 ………………(1)

On putting n = 1 in eq 1,

a1= 5(1) – 7

a1 = 5 - 7

a1 = -2

On putting n = 2 in eq 1,  

a2 = 5(2) – 7

a2 = 10 - 7

a2 = 10 – 7  

a2 = 3

On putting n = 3 in eq 1,

a3  = 5(3) – 7

a3  = 15 - 7

a3 = 8

 

Common difference, d1= a2 – a1

d1= 3 – (-2)  

d1 = 3 +2

d1 = 5

 

Common difference, d2= a3 – a2

d2 = 8 – 3  

d2 = 5

Since,  Common difference d1 & d2 are equal i.e d1 = d2 = 5

Hence, the given sequence is an A.P.

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