Find the 8th term of an exponential sequence whose first term is 3 and whose common ratio is 2
nth term=ar^(n-1)
8th term=ar^7=3*2^7=3*128=384
Answer is 384
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The answer is 215
To find the 8th term of an exponential sequence, we need to use the formula for the nth term of an exponential sequence:
𝑎𝑛 = 𝑎₁ × 𝑟^(𝑛−1)
Where:
𝑎𝑛 - represents the nth term of the sequence
𝑎₁ - represents the first term of the sequence
𝑟 - represents the common ratio of the sequence
𝑛 - represents the position of the term in the sequence
In this case, the first term (𝑎₁) is 3, and the common ratio (𝑟) is 2. We want to find the 8th term (𝑎₈).
Using the formula, we substitute the values into the equation:
𝑎₈ = 3 × 2^(8−1)
Simplifying the exponent:
𝑎₈ = 3 × 2^7
Now, we calculate the value of 2^7:
𝑎₈ = 3 × 128
Finally, we multiply 3 by 128 to find the value of the 8th term:
𝑎₈ = 384
Therefore, the 8th term of the exponential sequence is 384.