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Question
Q#1
If 7 times the 7th term of an A.P is equal to 11 times its 11th term, show that the 18th term of an A.P is Zero.

Q#2
If the 9th term of an A.P is Zero. Prove that its 29th term is twice its 19th term.

1)

Let the first term be a and the common difference d

The 7th term is a+6d

The 11th term is a+10d

7 times the 7th term is 7a+42d

11 times the 11th term is 11a+110d

so 7a+42d = 11a+110d and then

-4a = 68d

-a  = 17d

a = -17d

The 18th term is a + 17d

Since a = -17d ,

The 18th term is a + 17d  = -17d + 17d = 0

2)

Let the first term be a and the common difference d

The 9th term will be a + 8d

a + 8d = 0

a = -8d

The 29th term is a + 28d

The 19th term is a + 18d

Since a = -8d

The 29th term is -8d + 28d  = 20d

The 19th term is -8d + 18d  = 10d

So the 29th term is twice the 19th term  , 20d = (2)(10d)

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#### Socrates

##### Expertise

I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

##### Experience

Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.

Education/Credentials
B.S. , M.S. , Ph.D.