# Sequences.. ?

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• Nov 8th 2007, 03:21 AM
cu4mail
Sequences.. ?
Dear All,

I need help to solve these questions on sequences..

Q1. Write the first rour terms of the following sequences
If
i) $a_n = (-1)^n (2n-3)$

ii) $a_n - a_{n-1} = n + 2, a_1 = 2$

Q2. Which term of the arithmetic sequence -2, 4, 10, .... is 148?

Q3. Find the 11th term of the sequence 1+i, 2, 4/1+i, .... where i^2 = -1

Answers with some description will help me to understand the methodology.

Thanks in Advance
• Nov 8th 2007, 04:47 AM
kalagota
Quote:

Originally Posted by cu4mail
Dear All,

I need help to solve these questions on sequences..

Q1. Write the first rour terms of the following sequences
If
i) $a_n = (-1)^n (2n-3)$

ii) $a_n - a_{n-1} = n + 2, a_1 = 2$

all you have to do is to replace n by 1, 2, 3, and 4..

Quote:

Originally Posted by cu4mail
Q2. Which term of the arithmetic sequence -2, 4, 10, .... is 148?

note that $a_n = a_1 + (n-1)d$, where d is the common difference.. you see in the sequence that $a_1 = -2$ and d=6. so,
$a_n = 146 = -2 + (n-1)6$. solve for n.

Quote:

Originally Posted by cu4mail
Q3. Find the 11th term of the sequence 1+i, 2, 4/1+i, .... where i^2 = -1

Answers with some description will help me to understand the methodology.

Thanks in Advance

note that $\frac{2}{1+i} = \frac{\frac{4}{1+1}}{2}$ so that the sequence is Geometric..
so use the formula $a_n = a_1 r^{n-1}$, where r is the common ratio..
• Nov 8th 2007, 06:02 AM
Plato
Quote:

Originally Posted by kalagota
note that $\frac{2}{1+i} = \frac{\frac{4}{1+1}}{2}$ so that the sequence is Geometric..
so use the formula $a_n = a_1 r^{n-1}$, where r is the common ratio..

Actually $\frac{2}{1+i} = { 1-i }$