Question
Download Solution PDFTaking the first term of an A.P. to be α, the sum of first m terms is zero, then the sum of next n terms will be
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
Sum of first n terms of A.P
Sn = n/2[2a + (n - 1)d]
Calculation:
First term = a
Sm = 0
∴ m/2[2a + (m - 1)d] = 0
d = -2a/(m - 1) ---(i)
am + 1 = a + md
And md will be the first term for next n terms
Sn = n/2[2a + (n - 1)d]
Sn = n/2[2(a + md) + (n - 1)d]
⇒ n/2[2a + 2md + (n - 1)d]
⇒ n/2[2a + (2m + n - 1)d]
Put d from (i),
⇒ n/2[2a + (2m + n - 1)(-2a/(m - 1))]
n/2 × 2a [1 - (2m + n - 1)/(m - 1)]
⇒ an[(m - 1 - 2m - n + 1)/(m - 1)]
∴ Sm = an(n + m)/(1 - m)
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