Question

Which term of the sequence 2,4,6,......512 is 256?​

Answer 1

Answer:

If this sequence is part of an arithmetic sequence, then its 128-th term would be 256.

Step-by-step explanation:

The two neighboring terms differ by a constant, 2. As a result, this sequence is likely an arithmetic sequence.

• The first term $a_1$ is equal to 2.
• The common difference $d$ (second term - first term) is equal to 2.

The formula for the general $n$-th term of an arithmetic sequence with first term $a_1$ and common difference $d$ is:

$a_1 + (n - 1) \, d$.

In this case, that's equal to

$2 + (n - 1) \times 2 = 2 + 2 \times (n - 1) = 2\, n$.

Let that expression be equal to $256$. Solve for $n$:

$2\, n = 256$

$n = 128$ (after dividing both sides by $2$.)

Hence, if this sequence is part of an arithmetic sequence, then the 128-th term would be 256.

Answer 2

Answer:

128

Step-by-step explanation:

Givens

a = 2

L = 256

d = 2

n = ?

Formula

L = a + (n - 1)*d

Solution

256 = 2 + (n - 1)*2       Subtract 2 from both sides

254 = (n - 1)*2              Divide by 2    

254/2 = n-1)*2/2           Do the division  

127 = n - 1                     Add 1 to both sides..  

128 = n