Question

if the sum of first m tearms of an A.P. be n and the sum of first n tearm of the same A.P. be m , determine the sum of its (m+n) terms is​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

sum of 1st m terms = n

n = m[a+(m-1)d]/2

n = (ma + m²d - md)/2

sum of 1st n terms = m

m = n[a+(n-1)d]/2

m = (na + n²d - nd)/2

so, (m+n) = [(ma + m²d - md)+(na + n²d - nd)] / 2

(m+n) = (ma+na+m²d+n²d-md-nd) / 2

(m+n) = [a(m+n) +d(m²+n²) -d(m+n)]/2

(m+n) = [a(m+n) +d(m²-m+n²-n)] / 2