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

What is the fourth term of the sequence?

Sagot :

GinnyAnswer
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].
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