eattern is \( 5,10,20,40 \ldots \). Find the 8 th term of the pattern

The given pattern is \( 5, 10, 20, 40, \ldots \). To identify the pattern, let's analyze the terms: - The first term is \( 5 \). - The second term is \( 10 \) which is \( 5 \times 2 \). - The third term is \( 20 \) which is \( 10 \times 2 \). - The fourth term is \( 40 \) which is \( 20 \times 2 \). From this, we can see that each term is obtained by multiplying the previous term by \( 2 \). Thus, the \( n \)-th term can be expressed as: \[ a_n = 5 \times 2^{(n-1)} \] Now, we need to find the 8th term, \( a_8 \): \[ a_8 = 5 \times 2^{(8-1)} = 5 \times 2^7 \] Now, let's calculate \( 2^7 \): \[ 2^7 = 128 \] Now, substituting back: \[ a_8 = 5 \times 128 = 640 \] Therefore, the 8th term of the pattern is \( 640 \).