Final answer:
In an arithmetic sequence, with 13 messages received on day 3 and 64 on day 20, Linda received 40 messages on day 12 and will receive 154 messages on day 50. The first answer, option a is 40 messages, r option b is 154 messages.
Step-by-step explanation:
The question posed by the student involves an arithmetic sequence. Linda received 13 messages on day 3 and 64 messages on day 20.
To solve part a), we first need to find the common difference (d) of the arithmetic sequence. This can be calculated as follows:
- Number of terms between day 3 and day 20 is 20 - 3 = 17.
- Difference in the number of messages is 64 - 13 = 51.
- The common difference (d) is therefore 51 messages / 17 terms = 3 messages per day.
Now, we can find the number of messages on day 12 by:
- Calculating the number of terms from day 3 to day 12, which is 12 - 3 = 9.
- Adding 9 terms worth of the common difference to the message count on day 3: 13 + (9 * 3) = 13 + 27 = 40 messages.
To solve part b), calculate how many terms are between day 3 and day 50:
- Day 50 would be the 48th term from day 3 (50 - 3 = 47) since the sequence starts at day 1.
- Then multiply the common difference by 47 and add it to the message count on day 3: 13 + (47 * 3) = 13 + 141 = 154 messages.
Thus:
- On day 12, Linda received 40 messages.
- On day 50, Linda received 154 messages.