PLEASE HELP! NUMBER TWO PLEASE!! PLEASE SHOW ME HOW YOU DID IT! THANK YOU BUNCHES xoxo
1 answer:
Answer:
I will demonstrate the first two for you. The answer is 6, <u>30</u>, <u>54</u>, <u>78</u>, 102.
The answer to the second question is -3,<u> 21,</u> <u>45</u>, <u>63,</u> 93.
Step-by-step explanation:
Pardon the messiness. I hope this clarifies how to do it from now on! If not, please let me know if you need more help! xoxo
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Given:
The different recursive formulae.
To find:
The explicit formulae for the given recursive formulae.
Solution:
The recursive formula of an arithmetic sequence is and the explicit formula is
, where a is the first term and d is the common difference.
The recursive formula of a geometric sequence is and the explicit formula is
, where a is the first term and r is the common ratio.
The first recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:
Therefore, the correct option is A, i.e., .
The second recursive formula is:
for
.
It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is F, i.e., .
The third recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is D, i.e., .