Question

The sum of third and seventh
term of an Ap is 6 and their
product is 8 then find first term and common difference of A.P.
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Answer 1

Answer:

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=2