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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:

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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.

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