Nth term of 3,4,5,6,7,

Nth term of 3,4,5,6,7,

Answer :

Arithmetic Sequnce

To find the common difference, we may use the formula:
d = ?f=%5Cfrac%7Ba k%20 %20a m%7D%7Bk%20 %20m%7D (in whick ‘k’ is the higher term)
d = ?f=%5Cfrac%7B4%20 %203%7D%7B2%20 %201%7D
d = ?f=%5Cfrac%7B1%7D%7B1%7D
d = 1

Substitute the given values in the formula:
?f=a %7Bn%7D = ?f=a %7B1%7D + (n-1) d
?f=a %7Bn%7D = 3 + (n-1) 1
?f=a %7Bn%7D = 3 + (n-1)
?f=a %7Bn%7D = 3 + n – 1
?f=a %7Bn%7D = n + 2

Proving:
?f=a %7Bn%7D = n + 2
?f=a %7B2%7D = 2 + 2
?f=a %7B2%7D = 4 ✔

Thus, the nth term is equal to n + 2

 

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