To find the 15th term of the sequence 88, 92, 96, 100, we first identify the pattern in the sequence.
The sequence increases by 4 each time:
- 88 to 92: increase of 4
- 92 to 96: increase of 4
- 96 to 100: increase of 4
This means the sequence is an arithmetic progression (AP) where:
- The first term \( a = 88 \)
- The common difference \( d = 4 \)
The formula for the \( n \)-th term of an arithmetic sequence is given by: \[ a_n = a + (n - 1) \cdot d \]
To find the 15th term (\( n = 15 \)): \[ a_{15} = 88 + (15 - 1) \cdot 4 \] \[ a_{15} = 88 + 14 \cdot 4 \] \[ a_{15} = 88 + 56 \] \[ a_{15} = 144 \]
Therefore, the 15th term of the sequence is 144.