How can i find sum of series whose difference are in ap

Dear Student,

Let S = a + b + c + d + e + f + ….. Tn is a series how difference of terms are in AP, then
S = a + b + c + d + e+ … Tn-1 + Tn (Now substract the two equations)
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0 = a + {(b-a) + (c-b) + (d-c) + (e-d) + (f-e)+ ...+(z-y)} – Tn
From here now you can easily find Tn, then use the summation operator to find the sum of such series.

Thanks.