0000:00:00:00:00Start4Number 4ExplanationGiven the following number sequence: 1,4,5,9,14,…,37,60,971, 4, 5, 9, 14, \dots, 37, 60, 971,4,5,9,14,…,37,60,97 Which value correctly fills the blank in the sequence?232323242424252525262626272727ExplanationTo find the missing value, let's analyze the summation pattern between terms (Fibonacci Pattern): 3rd Term:1+4=54th Term:4+5=95th Term:5+9=14\begin{array}{rclcl} \text{3rd Term} & : & 1 + 4 & = & 5 \\ \text{4th Term} & : & 4 + 5 & = & 9 \\ \text{5th Term} & : & 5 + 9 & = & 14 \\ \end{array}3rd Term4th Term5th Term:::1+44+55+9===5914 The pattern formed is that each term is the sum of the two preceding terms (Un=Un−1+Un−2U_n = U_{n-1} + U_{n-2}Un=Un−1+Un−2). Based on this pattern, the value of the 6th term is: U6=U5+U4=14+9=23U_6 = U_5 + U_4 = 14 + 9 = 23U6=U5+U4=14+9=23 Let's verify this pattern for the subsequent terms: 7th Term:23+14=37✓8th Term:37+23=60✓9th Term:60+37=97✓\begin{array}{rclcl} \text{7th Term} & : & 23 + 14 & = & 37 \quad \checkmark \\ \text{8th Term} & : & 37 + 23 & = & 60 \quad \checkmark \\ \text{9th Term} & : & 60 + 37 & = & 97 \quad \checkmark \\ \end{array}7th Term8th Term9th Term:::23+1437+2360+37===37✓60✓97✓ Since the pattern is consistent through the end of the sequence, the correct value is 232323.
4Number 4ExplanationGiven the following number sequence: 1,4,5,9,14,…,37,60,971, 4, 5, 9, 14, \dots, 37, 60, 971,4,5,9,14,…,37,60,97 Which value correctly fills the blank in the sequence?232323242424252525262626272727ExplanationTo find the missing value, let's analyze the summation pattern between terms (Fibonacci Pattern): 3rd Term:1+4=54th Term:4+5=95th Term:5+9=14\begin{array}{rclcl} \text{3rd Term} & : & 1 + 4 & = & 5 \\ \text{4th Term} & : & 4 + 5 & = & 9 \\ \text{5th Term} & : & 5 + 9 & = & 14 \\ \end{array}3rd Term4th Term5th Term:::1+44+55+9===5914 The pattern formed is that each term is the sum of the two preceding terms (Un=Un−1+Un−2U_n = U_{n-1} + U_{n-2}Un=Un−1+Un−2). Based on this pattern, the value of the 6th term is: U6=U5+U4=14+9=23U_6 = U_5 + U_4 = 14 + 9 = 23U6=U5+U4=14+9=23 Let's verify this pattern for the subsequent terms: 7th Term:23+14=37✓8th Term:37+23=60✓9th Term:60+37=97✓\begin{array}{rclcl} \text{7th Term} & : & 23 + 14 & = & 37 \quad \checkmark \\ \text{8th Term} & : & 37 + 23 & = & 60 \quad \checkmark \\ \text{9th Term} & : & 60 + 37 & = & 97 \quad \checkmark \\ \end{array}7th Term8th Term9th Term:::23+1437+2360+37===37✓60✓97✓ Since the pattern is consistent through the end of the sequence, the correct value is 232323.
