If in the following series, `a_(1)=5, a_(2)= 9, a_(3)=13` and so on, then find the value of `a_(8), 5, 9, 13, …, a_(8)`

Options

A. 34
B. 33
C. 36
D. 35

Answer

To find the value of \( a_8 \) in the series where \( a_1 = 5 \), \( a_2 = 9 \), \( a_3 = 13 \), we can follow these steps:

### Step 1: Identify the pattern in the series
The given series is:
- \( a_1 = 5 \)
- \( a_2 = 9 \)
- \( a_3 = 13 \)

We can observe that each term increases by a constant value.

### Step 2: Calculate the common difference
To find the common difference \( d \), we can subtract the first term from the second term:
\[ d = a_2 - a_1 = 9 - 5 = 4 \]
We can also check the difference between the second and third terms:
\[ d = a_3 - a_2 = 13 - 9 = 4 \]
Thus, the common difference \( d \) is \( 4 \).

### Step 3: Use the formula for the nth term of an arithmetic progression
The formula for the nth term of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step 4: Substitute the values to find \( a_8 \)
Now, we need to find \( a_8 \):
- Here, \( a = 5 \),
- \( d = 4 \),
- \( n = 8 \).

Substituting these values into the formula:
\[ a_8 = 5 + (8 - 1) \cdot 4 \]
Calculating \( (8 - 1) \cdot 4 \):
\[ a_8 = 5 + 7 \cdot 4 \]
\[ a_8 = 5 + 28 \]
\[ a_8 = 33 \]

### Final Answer
Thus, the value of \( a_8 \) is \( 33 \).

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