urlchan
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The 15th term of an arithmetic sequence is 21 and the common difference is -4.
(a) Find the first term of the sequence.
(b) Find the 29th term of the sequence.
(c) Find the sum of the first 40 terms of the sequence.

Sagot :

praiseohlord

Answer:

a. Firat term of the sequence= 77

b. 29th term of the sequence= -35

c. Sum of the first 40 terms of the sequence= -40

Step-by-step explanation:

View image praiseohlord

The first term of the sequence is 77, the 29th term of the sequence is -35 and the sum of the first 40 terms of the sequence is -40.

Given that, [tex]a_{15} =21[/tex] and d=-4.

What is the nth term of the arithmetic sequence?

The nth term of the arithmetic sequence is [tex]a_{n} =a+(n-1)d[/tex].

To find the first term of the sequence:

[tex]a_{15}[/tex]=a+(15-1)(-4)

⇒21=a+(15-1)(-4)

⇒a=77

To find the 29th term of the sequence:

[tex]a_{29}[/tex]=77+(29-1)(-4)=-35

To find the sum of the first 40 terms of the sequence:

The first n terms of a sequence [tex]=\frac{n}{2}[2a+(n-1)d)][/tex]

[tex]S_{40} =\frac{40}{2}[2 \times77+(40-1)(-4))][/tex]

=20(154-156)=-40

Therefore, the first term of the sequence is 77, the 29th term of the sequence is -35 and the sum of the first 40 terms of the sequence is -40.

To learn more about the arithmetic sequence visit:

https://brainly.com/question/15412619.

#SPJ2

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.