1. ## Algebra

Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks

2. $S_n$ is defined by $S_n= \frac{1}{6}n(n+1)(n+2)$ so $S_{n-1}= \frac{1}{6}(n-1)((n-1)+ 1)((n-1)+ 2)= \frac{1}{6}(n-1)(n)(n+1)$

You could multiply both of those out and subtract but it is simpler to notice that each has factors of 1/6, n, and n+1 andfactor those out:
$S_{n}- S_k{n-1}= \frac{1}{6}(n)(n+1)(n+2- (n-1))= \frac{1}{6}n(n+1)(3)$

3. ## sequence oroblem

Originally Posted by igcsestudent
Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks
sequence 1,4,10,20,35 Find nextterm
Differences 3,6,10, 15, next difference is 21 6 comes after 3,4,5
35+21 is 56

bjh

4. cool!
The text contains multiple posts, each with a mathematical question or a response to a question. One post provides a sequence problem and its solution, while another post provides a detailed algebraic explanation.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
1. ## Algebra

Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks

2. $S_n$ is defined by $S_n= \frac{1}{6}n(n+1)(n+2)$ so $S_{n-1}= \frac{1}{6}(n-1)((n-1)+ 1)((n-1)+ 2)= \frac{1}{6}(n-1)(n)(n+1)$

You could multiply both of those out and subtract but it is simpler to notice that each has factors of 1/6, n, and n+1 andfactor those out:
$S_{n}- S_k{n-1}= \frac{1}{6}(n)(n+1)(n+2- (n-1))= \frac{1}{6}n(n+1)(3)$

3. ## sequence oroblem

Originally Posted by igcsestudent
Hello,
can any "smart" person who is very good at math solve this question? it is (d) in the attachment....
good luck
thanks
sequence 1,4,10,20,35 Find nextterm
Differences 3,6,10, 15, next difference is 21 6 comes after 3,4,5
35+21 is 56

bjh

4. cool!
user
The text contains multiple posts, each with a mathematical question or a response to a question. One post provides a sequence problem and its solution, while another post provides a detailed algebraic explanation.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS