# Thread: Find the sum of the first 5 terms of sequence

1. ## Find the sum of the first 5 terms of sequence

Please help, I'm understanding some parts of the sequence and then some parts are confusing. I remember doing these in algebra but they were much simpler. I thought I only had to plug & chug, but...

I need help with finding the sum of the first 5 terms of the sequence and they are defined recursively by:

$\displaystyle a_{1}=1; a_{2}= 2; \ a_{n}= \ a^2_{n-1} + a^2_{n-2}, \ n\geq3$;

The sum is 1 + 2 + 5 + 29 + 866 = 903.

I thought the way to do this was to replace n with the numbers 1 - 5:

$\displaystyle a_{1}= a^2_{2-1} + a^2_{2-2} = 1$ to get the sum, what I was wrong.

If I plug in '2' for the next sequence I don't get the right answer. How do I plug in the numbers and solve. I'm confused, please help! TIA...

2. Originally Posted by lilrhino
Please help, I'm understanding some parts of the sequence and then some parts are confusing. I remember doing these in algebra but they were much simpler. I thought I only had to plug & chug, but...

I need help with finding the sum of the first 5 terms of the sequence and they are defined recursively by:

$\displaystyle a_{1}=1; a_{2}= 2; \ a_{n}= \ a^2_{n-1} + a^2_{n-2}, \ n\geq3$;

The sum is 1 + 2 + 5 + 29 + 866 = 903.

I thought the way to do this was to replace n with the numbers 1 - 5:

$\displaystyle a_{1}= a^2_{2-1} + a^2_{2-2} = 1$ to get the sum, what I was wrong.

If I plug in '2' for the next sequence I don't get the right answer. How do I plug in the numbers and solve. I'm confused, please help! TIA...
you are already given a_1 and a_2, no need to find them. all you need to do is find the next 3 terms. so plug in n = 3,4,5 one at a time, and add up all the terms you get with the terms given for a_1 and a_2

3. Originally Posted by Jhevon
you are already given a_1 and a_2, no need to find them. all you need to do is find the next 3 terms. so plug in n = 3,4,5 one at a time, and add up all the terms you get with the terms given for a_1 and a_2
I tried to do $\displaystyle a_{4}$ but when I plugged in '4' it didn't equal '29'. I got $\displaystyle 3^2 + 2^2 \ which = 13$ not 29. Still don't get what I'm doing wrong...

4. Originally Posted by lilrhino
I tried to do $\displaystyle a_{4}$ but when I plugged in '4' it didn't equal '29'. I got $\displaystyle 3^2 + 2^2 \ which = 13$ not 29. Still don't get what I'm doing wrong...
$\displaystyle a_3 = 5$

so $\displaystyle a_4 = a_{4 - 1}^2 + a_{4 - 2}^2 = a_3^2 + a_2^2 = 5^2 + 2^2 = 29$

5. Originally Posted by Jhevon
$\displaystyle a_3 = 5$

so $\displaystyle a_4 = a_{4 - 1}^2 + a_{4 - 2}^2 = a_3^2 + a_2^2 = 5^2 + 2^2 = 29$
Thanks for your response Jhevon -- I got it!