# Math Help - Sequences.. ?

1. ## 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.

2. 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..

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.

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.

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