1. ## Geometric sequence

Write the expression for the nth term of the geometric sequence. Then find the 20th term of the sequence.

a1= 100, r= 1.05

2. Hi thepride

Do you know the general fomula for the nth term of the geometric sequence?

3. Originally Posted by thepride
Write the expression for the nth term of the geometric sequence. Then find the 20th term of the sequence.

a1= 100, r= 1.05
$\displaystyle 100 * 1.05^n$

$\displaystyle 100 * 1.05^20 = 265.3297705$

Therefore the 20th term is 265.3297705

Note. The 1.05^20 means 1.05 times itself 20 times.

4. Originally Posted by Barthayn
$\displaystyle 100 * 1.05^n$

$\displaystyle 100 * 1.05^20 = 265.3297705$

Therefore the 20th term is 265.3297705

Note. The 1.05^20 means 1.05 times itself 20 times.
i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
?
im not sure though can someone check my work?

5. Originally Posted by thepride
i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
?
im not sure though can someone check my work?

HI

indeed

$\displaystyle T_20=100(1.05)^{19}$

6. Originally Posted by thepride
i dont think that is right barthayn. its more like an= 100(1.05)^n-1 which is about 252.695
?
im not sure though can someone check my work?
well if you look the formula is An= A1*1.05^n-1
so you would plug in An= 100*1.05^(20-1) which is the given answer in your book.

7. yeah, Flexus is right, I forgot to subtract n by one. You have to n-1 because 1.05 counts for the first one.