Question

if mth term of AP is n then nth term of AP is m then find the first term
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Answer 1

Answer:

a = m+n-1

Step-by-step explanation:

let 1st term = a and common difference = d

mth term = tm = a+(m-1)d = n

nth term = tn = a+(n-1)d = m

tm - tn = {a+(m-1)d} - {a+(n-1)d} = n - m

=> a+(m-1)d - a-(n-1)d = n-m

=> (m-1-n+1)d = n-m

=> (m-n)d = -(m-n)

=> d = -(m-n)/(m-n) = -1

a+(m-1)d = n

=> a+(m-1)(-1) = n

=> a-m+1 = n

=> a = m+n-1