InterviewSolution
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InterviewSolution
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is 0.If m times the mth term of an AP is equal to n times the nth term and mterm is 0n, show that its (m+n-thracudinit numhers are divisible by 7? |
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Answer» Let the first term of AP = acommon difference = dWe have to show that (m+n)th term is zero ora + (m+n-1)d = 0 mth term= a + (m-1)dnth term = a + (n-1) d Given thatm{a +(m-1)d} = n{a + (n -1)d}⇒am +m²d -md = an + n²d - nd⇒am - an +m²d - n²d -md + nd = 0⇒a(m-n) + (m²-n²)d-(m-n)d = 0⇒a(m-n) + {(m-n)(m+n)}d -(m-n)d = 0⇒ a(m-n) + {(m-n)(m+n) -(m-n)} d = 0⇒a(m-n) +(m-n)(m+n -1) d = 0⇒ (m-n){a+ (m+n-1)d} = 0⇒a + (m+n -1)d = 0/(m-n)⇒a + (m+n -1)d = 0 |
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