If the first term in an arithmetic sequence is 15 and the tenth term is 69. What is the fourth term in the sequence?
"first term in an arithmetic sequence is 15" ---> a=15
"the tenth term is 69" ---> a+9d = 69
sub in a = 15 to find d
then evaluate
a + 3d
how do we sub it in and evaluate
really?
You are studying the above topic and you are asking this question?
Sorry, but .....
by now I'm sure you have figured out what it means to substitute a value, but just in case, that gives you
15+9d = 69
Now you can get d, and thus a+3d.
Is the term 33
The 10th term in an arithmetic sequence is 8 and the 4th term is -4. Determine the first term a.
To find the fourth term in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
𝑎𝑛 = 𝑎₁ + (𝑛 − 1)𝑑
Where:
𝑎𝑛 is the nth term
𝑎₁ is the first term
𝑛 is the position of the term in the sequence
𝑑 is the common difference between each term
We are given that the first term (𝑎₁) in the sequence is 15, and the tenth term (𝑎₁₀) is 69. We need to find the fourth term (𝑎₄).
To find the common difference (𝑑), we can subtract the first term (𝑎₁) from the tenth term (𝑎₁₀) and divide by 9 (the number of terms between them):
𝑑 = (𝑎₁₀ - 𝑎₁) / 9
Substituting the values we know:
𝑑 = (69 - 15) / 9
𝑑 = 54 / 9
𝑑 = 6
Now, we can substitute the values of 𝑎₁, 𝑑, and 𝑛 into the formula to find the fourth term (𝑎₄):
𝑎₄ = 𝑎₁ + (𝑛 − 1)𝑑
𝑎₄ = 15 + (4 - 1)6
𝑎₄ = 15 + 3(6)
𝑎₄ = 15 + 18
𝑎₄ = 33
Therefore, the fourth term in the arithmetic sequence is 33.