0000:00:00:00:00Start3Number 3ExplanationGiven the following number sequence: 4,6,10,9,11,15,14,…4, 6, 10, 9, 11, 15, 14, \dots4,6,10,9,11,15,14,… Which value correctly completes the sequence?151515161616171717181818191919ExplanationTo find the next value, let's analyze the pattern between the terms in the sequence: 4→+26(1st to 2nd term)6→+410(2nd to 3rd term)10→−19(3rd to 4th term)9→+211(4th to 5th term)11→+415(5th to 6th term)15→−114(6th to 7th term)\begin{array}{ccl} 4 \xrightarrow{+2} 6 & \quad & (\text{1st to 2nd term}) \\ 6 \xrightarrow{+4} 10 & \quad & (\text{2nd to 3rd term}) \\ 10 \xrightarrow{-1} 9 & \quad & (\text{3rd to 4th term}) \\ 9 \xrightarrow{+2} 11 & \quad & (\text{4th to 5th term}) \\ 11 \xrightarrow{+4} 15 & \quad & (\text{5th to 6th term}) \\ 15 \xrightarrow{-1} 14 & \quad & (\text{6th to 7th term}) \end{array}4+266+41010−199+21111+41515−114(1st to 2nd term)(2nd to 3rd term)(3rd to 4th term)(4th to 5th term)(5th to 6th term)(6th to 7th term) We can see that the pattern is a repeating cycle of operations: +2,+4,−1+2, +4, -1+2,+4,−1. Based on this pattern, the operation following −1-1−1 cycles back to +2+2+2. Therefore, the next term is: 14+2=1614 + 2 = 1614+2=16 Thus, the correct value to complete the sequence is 161616.
3Number 3ExplanationGiven the following number sequence: 4,6,10,9,11,15,14,…4, 6, 10, 9, 11, 15, 14, \dots4,6,10,9,11,15,14,… Which value correctly completes the sequence?151515161616171717181818191919ExplanationTo find the next value, let's analyze the pattern between the terms in the sequence: 4→+26(1st to 2nd term)6→+410(2nd to 3rd term)10→−19(3rd to 4th term)9→+211(4th to 5th term)11→+415(5th to 6th term)15→−114(6th to 7th term)\begin{array}{ccl} 4 \xrightarrow{+2} 6 & \quad & (\text{1st to 2nd term}) \\ 6 \xrightarrow{+4} 10 & \quad & (\text{2nd to 3rd term}) \\ 10 \xrightarrow{-1} 9 & \quad & (\text{3rd to 4th term}) \\ 9 \xrightarrow{+2} 11 & \quad & (\text{4th to 5th term}) \\ 11 \xrightarrow{+4} 15 & \quad & (\text{5th to 6th term}) \\ 15 \xrightarrow{-1} 14 & \quad & (\text{6th to 7th term}) \end{array}4+266+41010−199+21111+41515−114(1st to 2nd term)(2nd to 3rd term)(3rd to 4th term)(4th to 5th term)(5th to 6th term)(6th to 7th term) We can see that the pattern is a repeating cycle of operations: +2,+4,−1+2, +4, -1+2,+4,−1. Based on this pattern, the operation following −1-1−1 cycles back to +2+2+2. Therefore, the next term is: 14+2=1614 + 2 = 1614+2=16 Thus, the correct value to complete the sequence is 161616.
