Geometric and Arithmetic Sequence

**ferken** · January 8th 2009, 04:55 PM

Hi im a bit confused about these questions here. I do not know where to start, but much help is appreciated.

Question 1

In an arithmetic sequence t4 + t5 + t6 = 300 and t15 + t16 + t17 = 201
Find t18

Question 2

In a geometric sequence t1 + t2 + t3 = 21 and t4 + t5 + t6 = 168
Find the squence

Thanks in advance =]

**red_dog** · January 9th 2009, 01:00 AM

In an arithmetic sequence $t_n=t_1+(n-1)r$
In a geometric sequence $t_n=t_1r^{n-1}$

Write the equations in terms of $t_1$ and $r$ , then solve the systems.

**Chop Suey** · January 9th 2009, 02:01 AM

Another way for the first one.

The n-th term of an arithmetic sequence is given by $t_n = t_m + (n-m)d$ where n > m and d is common difference.

You are given the sum of consecutive odd-numbered terms. The arithmetic mean of these terms is the middle term. For instance:
$\frac{t_4+t_5+t_6}{3} = t_5$

Note that this applies only for the arithmetic sequence.

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