Answered

Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.

Find the [tex]\( n^{\text{th}} \)[/tex] term of the arithmetic sequence whose initial term is [tex]\( a_1 \)[/tex] and common difference is [tex]\( d \)[/tex]. What is the seventy-first term?

Given:
[tex]\[ a_1 = 3 \][/tex]
[tex]\[ d = -8 \][/tex]

Enter the formula for the [tex]\( n^{\text{th}} \)[/tex] term of this arithmetic series:
[tex]\[ a_n = \square \][/tex]

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Sagot :

GinnyAnsweridn
To find the [tex]\( n \)[/tex]-th term of an arithmetic sequence, we use the formula:

[tex]\[ a_n = a_1 + (n - 1) \cdot d \][/tex]

where [tex]\( a_1 \)[/tex] is the first term, [tex]\( d \)[/tex] is the common difference, and [tex]\( n \)[/tex] is the term number we want to find.

Given the values:
[tex]\[ a_1 = 3 \][/tex]
[tex]\[ d = -8 \][/tex]
and we want to find the [tex]\( 71 \)[/tex]-st term ([tex]\( n = 71 \)[/tex]).

First, let's substitute [tex]\( a_1 \)[/tex], [tex]\( d \)[/tex], and [tex]\( n \)[/tex] into the formula:

[tex]\[ a_{71} = 3 + (71 - 1) \cdot (-8) \][/tex]

Simplify the expression step by step:

1. Calculate [tex]\( 71 - 1 \)[/tex]:
[tex]\[ 71 - 1 = 70 \][/tex]

2. Multiply by the common difference [tex]\( d \)[/tex]:
[tex]\[ 70 \cdot (-8) = -560 \][/tex]

3. Add the result to the first term [tex]\( a_1 \)[/tex]:
[tex]\[ 3 + (-560) = 3 - 560 = -557 \][/tex]

Therefore, the seventy-first term [tex]\( a_{71} \)[/tex] of the arithmetic sequence is:

[tex]\[ a_{71} = -557 \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.