5. Write down the next three terms in each of the following sequences: \( 5.1,2,5,7,10 \), ...m. , ...m.. , ......

To find the next three terms in the sequence \( 2, 5, 7, 10 \), we first need to identify the pattern. Let's look at the differences between the terms: - From \( 2 \) to \( 5 \): \( 5 - 2 = 3 \) - From \( 5 \) to \( 7 \): \( 7 - 5 = 2 \) - From \( 7 \) to \( 10 \): \( 10 - 7 = 3 \) The differences are \( 3, 2, 3 \). It seems like the pattern alternates between adding \( 3 \) and \( 2 \). Continuing this pattern: - From \( 10 \), we add \( 2 \): \( 10 + 2 = 12 \) - From \( 12 \), we add \( 3 \): \( 12 + 3 = 15 \) - From \( 15 \), we add \( 2 \): \( 15 + 2 = 17 \) Thus, the next three terms in the sequence are \( 12, 15, 17 \). So, the complete sequence is: \( 2, 5, 7, 10, 12, 15, 17 \).