Question

if TN is the nth term of an AP then the value of tn+1 - tn-1​

Answer 1

Answer:

Step-by-step explanation:

we know the formula of nth term tₙ=a+(n-1)d,where a is the first term,d is the common difference and n is the number of terms

so similarly,we can write tₙ₋₁ =a+((n-1)-1)d = a+(n-2)d

also                                   tₙ₊₁=a+((n+1)-1)d = a+nd

so  tₙ₊₁ - tₙ₋₁ = (a+nd) - (a+(n-2)d)  = (a+nd) - (a+nd-2d)

= a+nd-a-nd+2d= 2d

so the answer is 2d where we can write d= tₙ₊₁ - tₙ or =  tₙ - tₙ₋₁ ,as d is the difference of two consecutive terms

so answer= 2d = 2(tₙ₊₁ - tₙ) or 2( tₙ - tₙ₋₁)

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