Answered

Join IDNLearn.com and start getting the answers you've been searching for. Discover reliable answers to your questions with our extensive database of expert knowledge.

The first term of an arithmetic sequence is 10, and its common difference is -7.

What is the fourth term of the sequence?

Sagot :

GinnyAnsweridn
To find the fourth term of an arithmetic sequence, we typically use the formula for the nth term of an arithmetic sequence:

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

where:
- [tex]\( a_n \)[/tex] is the nth term of the sequence,
- [tex]\( a_1 \)[/tex] is the first term of the sequence,
- [tex]\( d \)[/tex] is the common difference,
- [tex]\( n \)[/tex] is the term number.

In this problem:
- The first term [tex]\( a_1 = 10 \)[/tex],
- The common difference [tex]\( d = -7 \)[/tex],
- The term number [tex]\( n = 4 \)[/tex].

Now, let's substitute these values into the formula:

[tex]\[ a_4 = 10 + (4 - 1)(-7) \][/tex]

First, calculate the expression inside the parentheses:

[tex]\[ 4 - 1 = 3 \][/tex]

Next, multiply this result by the common difference:

[tex]\[ 3 \times (-7) = -21 \][/tex]

Finally, add this result to the first term:

[tex]\[ a_4 = 10 + (-21) \][/tex]

This simplifies to:

[tex]\[ a_4 = 10 - 21 = -11 \][/tex]

Thus, the fourth term of the sequence is [tex]\( -11 \)[/tex].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.