AP - first five term and first ten terms are equal

Arithmetic and Geometric progressions.

AP - first five term and first ten terms are equal

Postby Jerome » Sat Mar 19, 2016 8:08 pm

The first term of an AP is 11 the first five term and first ten terms respectively are equal in magnitude but opposite in sign. find the second term.
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Re: AP

Postby Guest » Mon Mar 21, 2016 9:02 am

We know that:
[tex]a_1 = 11[/tex]
[tex]a_{10} = -a_5[/tex]

From the the formula for nth therm of an arithmetic progression we have:
[tex]a_{10} = a_1+(10-1)d = 11+9d[/tex]
[tex]a_5 = a_1+(5-1)d = 11+4d[/tex]

and since [tex]a_10 = -a_5[/tex]
11 + 9d = -(11+4d)
11 + 9d = -11 - 4d
9d + 4d = -11 - 11
13d = -22
[tex]d = -\frac{22}{13}[/tex]

the second therm is [tex]a_1 + d = 11 - \frac{22}{13} = \frac{121}{13}[/tex]
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