Question

what is the common difference of an A. P. in which a21-a7=84

Answer 1

a21 is a+20d
a7 is a+ 6d
when a21-a7 =84 then
a+20d -(a +6d) =84
a+20d-a-6d=84
14d=84
d=6

Answer 2

Answer:

d = 6

Step-by-step explanation:

  We know, { aₙ = a + ( n - 1 ) d }

∴  a₂₁ = a + ( 21 - 1 ) d = a + 20d

→  a₇ = a + ( 7 + 1 ) d = a + 6d

Given a₂₁ - a₇ = 84 ⇒ [1]

Substituting in [1]

→ a + 20d - ( a + 6d ) = 84

→ a + 20d - a - 6d = 84

→  20d - 6d =84

→ 14d = 84

→ d = 84/14

→  d = 6

∴ common difference d = 6

Isn't it simple? All the best for your exams!!

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