jihoonsqt
Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Write the explicit formula for the arithmetic sequence below and use it to find the 52nd term: 25, 19, 13, 7

Sagot :

Nayefx

Answer:

[tex] \displaystyle \:a_n=- 6n + 31[/tex]

[tex] \displaystyle \:a_{52}= - 281[/tex]

Step-by-step explanation:

we are given some numbers

25,19,13,9

and said to figure out the sequence and 52 term

recall arithmetic sequence

[tex] \displaystyle \: a + (n - 1)d[/tex]

where a is the first term and d is the common difference

let's figure out d

[tex] \displaystyle \:d = 19 - 25 \\ d= - 6[/tex]

and a is 25

now we need to substitute the value of a and d and simplify to get our formula

substitute the value of a and d:

[tex] \displaystyle \: 25 + (n - 1) (- 6)[/tex]

distribute -6:

[tex] \displaystyle \: 25 + ( - 6n + 6)[/tex]

remove parentheses:

[tex] \displaystyle \: 25 - 6n + 6[/tex]

simplify addition:

[tex] \displaystyle \: - 6n + 31[/tex]

so our formula is -6n+31

remember here n means nth number term

we are said to figure out 52 number term

so

substitute the value of n:

[tex] \displaystyle \: - 6.52 + 31[/tex]

simplify multiplication:

[tex] \displaystyle \: - 312 + 31[/tex]

simplify addition:

[tex] \displaystyle \: - 281[/tex]

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.