What is the 10th term of the sequence 2,4 ,……….. ?

Options

A. 18
B. 20
C. 1024
D. can't be determined

Answer

To find the 10th term of the sequence 2, 4, ..., we first need to determine the nature of the sequence.

### Step 1: Identify the type of sequence
The given sequence is 2, 4, ... We need to check if it is an arithmetic progression (AP) or a geometric progression (GP).

### Step 2: Check for Arithmetic Progression (AP)
In an AP, the difference between consecutive terms is constant.

- First term (T1) = 2
- Second term (T2) = 4

Calculate the common difference (d):
\[ d = T2 - T1 = 4 - 2 = 2 \]

Since we have a common difference, this sequence is an arithmetic progression.

### Step 3: Find the nth term formula for AP
The nth term (Tn) of an arithmetic progression can be calculated using the formula:
\[ Tn = T1 + (n - 1) \cdot d \]

### Step 4: Substitute values to find the 10th term
We need to find the 10th term (T10):
- n = 10
- T1 = 2
- d = 2

Substituting these values into the formula:
\[ T10 = 2 + (10 - 1) \cdot 2 \]
\[ T10 = 2 + 9 \cdot 2 \]
\[ T10 = 2 + 18 \]
\[ T10 = 20 \]

### Conclusion
The 10th term of the sequence is 20.

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