find the 25th term of the arithmetic sequence 24, 19, 14, 9 ...
Subtract 5 each time. The 25th term will be a negative number.
a=24
d=-5
term(25) = a+24d = 24 + 24(-5) = -96
To find the 25th term of an arithmetic sequence, we need to find the common difference first.
The common difference (d) can be found by subtracting any two consecutive terms in the sequence. Let's subtract the second term (19) from the first term (24):
d = 19 - 24 = -5
Now that we know the common difference (d = -5), we can find the 25th term using the formula for arithmetic sequences:
an = a1 + (n - 1) * d
where:
an = the nth term
a1 = the first term
n = term number
Plugging in the known values:
a25 = 24 + (25 - 1) * -5
Simplifying:
a25 = 24 + 24 * -5
a25 = 24 - 120
a25 = -96
Therefore, the 25th term of the arithmetic sequence 24, 19, 14, 9 is -96.
To find the 25th term of an arithmetic sequence, you need to know the first term, the common difference, and the formula for the nth term.
In this sequence, the first term (a₁) is 24, and the common difference (d) is -5. The common difference is obtained by subtracting the second term from the first term.
Now, we can use the formula for the nth term of an arithmetic sequence, which is:
aₙ = a₁ + (n - 1)d
Where:
aₙ represents the nth term
a₁ represents the first term
n represents the term you want to find
d represents the common difference
Substituting the given values into the formula:
a₂₅ = 24 + (25 - 1)(-5)
Simplifying further:
a₂₅ = 24 + 24(-5)
a₂₅ = 24 - 120
a₂₅ = -96
Therefore, the 25th term of the arithmetic sequence is -96.