What is the 10th number in the sequence: 5, 11, 17, 23, 29, 35, ...?

To determine the 10th number in the sequence, we first need to observe the pattern of the given numbers: 5, 11, 17, 23, 29, 35. The differences between consecutive terms can be calculated as follows:

• From 5 to 11, the difference is 6.

• From 11 to 17, the difference is also 6.

• Continuing this, the differences remain consistent: 6, 6, 6, ...

This indicates that the sequence is an arithmetic sequence with a common difference of 6. We can express the nth term of an arithmetic sequence using the formula:

[ a_n = a_1 + (n-1) \cdot d ]

where:

• ( a_n ) is the nth term,

• ( a_1 ) is the first term (5 in this case),

• ( d ) is the common difference (6).

To find the 10th term (( n = 10 )), we can substitute these values into the formula:

[ a_{10} = 5 + (10-1) \cdot 6 ]

[ a_{10} = 5 + 9 \cd