Question

In AP -6,-3,0,3....... the frist term and common differences are respectively??

Answer 1

In arithmetic progressions,

a = first term

d = common difference

a₂ = a + ( 2 - 1 ) d = a + d second term

aₓ = a + ( x - 1 )d = x th term

In the given question,- 6 is the first term.

∴ - 6 = a

a₂ = - 3

a₃ = 0

We know that the common difference is the difference between any two consecutive terms of the AS, like common difference = aₓ - a₍ₓ₋₁₎ and it is common ( equal ) in all terms.

∴ Common difference between the given terms = a₃ - a₂ = a₂ - a₁

⇒ Common difference between the given terms = 0 -3 = - 3 -  (- 6 )

⇒ Common difference between the given terms = - 3 = - 3 + 6

⇒  Common difference between the given terms =  - 3 = - 3

As the difference is common in the terms, - 3 is the common difference.

∴ - 6 and - 3 is the first term and common difference of the given AP.

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