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The second term of an H.P. is 314 and fifth term is 110 . Find the sum of its 6th and 7th term then prove that 513/3233 |
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Answer» We have,Let first TERM is an A.P.a=−14Fifth term is a 5 =a+4d=2Put a=−14 and we get,a+4d=2−14+4d=24d=2+144d=16d=4Find the value of nWhose SUM is 40.Then,We KNOW that,S n = 2n (2a+(n−1)d)⇒40= 2n (2×(−14)+(n−1)×4)⇒80=n(−28+4n−4)⇒80=n(−32+4n)⇒4n(n−8)=80⇒n(n−8)=20⇒n 2 −8n−20=0⇒n 2 −(10−2)n−20=0⇒n 2 −10n+2n−20=0⇒n(n−10)+2(n−10)=0⇒(n−10)(n+2)=0Forn+2=0n=−2It is not possible (negative)For,n−10=0n=10Hence, this is the answer. |
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