Question

if an= -2n+5 is in A.P., then find the common difference

Answer 1

Firstly take n=1
therefore, -2n+5= -2×1+5= -2+5=3

Now take n=2
therefore, -2n+5= -2×2+5= -4+5= 1

So, common difference= 1-3 = -2

Answer 2

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here is your answer

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an = a+ (n-1)d

d = common difference

in this question :

an = -2n+5

then

a+ (n-1)d = -2n+5
a+nd-d = -2n + 5
(a-d)+nd = -2n + 5

then compare LHS and RHS:
a-d = 5
d = -2

a-d = 5
a+2 = 5
a = 3

then common difference = -2