If the first term in an arithmetic sequence is 15 and the tenth term is 69. What is the fourth term in the sequence?
To find the fourth term in an arithmetic sequence, we can use the formula:
𝑎𝑛 = 𝑎₁ + (𝑛 − 1) × 𝑑
where 𝑎𝑛 represents the 𝑛-th term, 𝑎₁ represents the first term, 𝑛 represents the position of the term we are interested in, and 𝑑 represents the common difference between terms.
Given that the first term (𝑎₁) is 15, let's substitute this value into the formula:
𝑎𝑛 = 15 + (𝑛 − 1) × 𝑑
Since we want to find the fourth term (𝑎₄), we substitute 𝑛 = 4:
𝑎₄ = 15 + (4 − 1) × 𝑑
Now, we need to determine the common difference (𝑑). A common difference can be found by subtracting any two consecutive terms in the sequence. In this case, we know the first term (15) and the tenth term (69). We can use these values to find 𝑑:
𝑑 = (𝑎₁₀ - 𝑎₁) / (10 - 1)
𝑑 = (69 - 15) / 9
𝑑 = 54 / 9
𝑑 = 6
Now, we can substitute 𝑑 = 6 back into the formula to find 𝑎₄:
𝑎₄ = 15 + (4 − 1) × 6
𝑎₄ = 15 + 3 × 6
𝑎₄ = 15 + 18
𝑎₄ = 33
Therefore, the fourth term in the arithmetic sequence is 33.
a=15
a+9d=69
so, find d, and then
T4 = a+3d