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The sum of the third and the seventh terms of an ap is 6 their product is 8 find the sum of first sixteen terms of an ap

Posted by Maneesh Shetty 4 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Yash Verma 4 years, 9 months ago

Let a and d be the first term and common difference of AP nth term of AP an=a+(n−1)d ∴a3=a+(3−1)d=a+2d a7=a+(7−1)d=a+6d Given a3+a7=6 ∴(a+2d)+(a+6d)=6 ⇒2a+8d=6 ⇒a+4d=3....(1) Also given a3×a7=8 ∴(a+2d)(a+6d)=8 ⇒(3−4d+2d)(3−4d+6d)=8 [Using (1)] ⇒(3−2d)(3+2d)=8 ⇒9−4d2=8 ⇒4d2=1 ⇒d2=41 ⇒d=±21 When d=21 a=3−4d=3−4×21=3−2=1 When d=−21 a=3−4d=3+4×21=3+2=5 When a=1 & d=21 S16=216[2×1+(16−1)×21]=8(2+215)=4×19=76 When a=5 & d=−21 S16=216[2×5+(16−1)×(−21)]=8(10−215)=4×5=20 Thus the sum of first 16 term of the ap is 7 or 20

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