Calcular los valores faltantes considerando los valores existentes en la progresión

1 = 
2 = 
3 = 
4 = 400
5 = 
6 =
7 =
8 =
9 =
10 = 600
11 =
12 =
13 = 
14 =
15 = 1000
16 = 
17 = 
18 = 
19 = 
20 = 1400
21 =
22 =
23 =
24 =
25 = 1800
26 =
27 =
28 =
29 =
30 = 2400
31 =
32 =
33 =
34 =
35 = 3000
36 =
37 =
38 =
39 =
40 = 3600
41 =
42 =
43 =
44 =
45 = 4400
46 =
47 =
48 =
49 =
50 = 5200
51 =
52 =
53 =
54 =
55 = 6000
56 =
57 =
58 =
59 =
60 = 6800
61 =
62 =
63 =
64 =
65 = 7800
66 =
67 =
68 =
69 =
70 = 8600
71 =
72 =
73 =
74 =
75 = 9800
76 =
77 =
78 =
79 =
80 = 10800
81 =
82 =
83 =
84 =
85 = 12800
86 =
87 =
88 =
89 =
90 = 13200
91 =
92 =
93 =
94 =
95 = 14600
96 =
97 =
98 =
99 =
100 = 15800
101 =
102 =
103 =
104 =
105 = 17000
106 =
107 =
108 =
109 =
110 = 18400
111 =
112 =
113 =
114 =
115 = 19800
116 =
117 =
118 =
119 =
120 = 21400
121 =
122 =
123 =
124 =
125 =23000
126 =
127 =
128 =
129 =
130 = 24600
131 =
132 =
133 =
134 =
135 = 26200
136 =
137 =
138 =
139 =
140 = 27800
141 =
142 =
143 =
144 =
145 = 29600
146 =
147 =
148 =
149 =
150 = 31400


Para calcular los valores faltantes en esta progresión, observemos primero los términos que ya tenemos y determinemos si hay un patrón específico.

Los términos dados son:
- \( a_4 = 400 \)
- \( a_{10} = 600 \)
- \( a_{15} = 1000 \)
- \( a_{20} = 1400 \)
- \( a_{25} = 1800 \)
- \( a_{30} = 2400 \)
- \( a_{35} = 3000 \)
- \( a_{40} = 3600 \)
- \( a_{45} = 4400 \)
- \( a_{50} = 5200 \)
- \( a_{55} = 6000 \)
- \( a_{60} = 6800 \)
- \( a_{65} = 7800 \)
- \( a_{70} = 8600 \)
- \( a_{75} = 9800 \)
- \( a_{80} = 10800 \)
- \( a_{85} = 12800 \)
- \( a_{90} = 13200 \)
- \( a_{95} = 14600 \)
- \( a_{100} = 15800 \)
- \( a_{105} = 17000 \)
- \( a_{110} = 18400 \)
- \( a_{115} = 19800 \)
- \( a_{120} = 21400 \)
- \( a_{125} = 23000 \)
- \( a_{130} = 24600 \)
- \( a_{135} = 26200 \)
- \( a_{140} = 27800 \)
- \( a_{145} = 29600 \)
- \( a_{150} = 31400 \)

Vamos a analizar estos términos para ver si hay un patrón en el incremento entre los valores.

Primero, calculemos las diferencias entre términos consecutivos:

\[ 
\begin{align*}
a_{10} - a_4 &= 600 - 400 = 200 \\
a_{15} - a_{10} &= 1000 - 600 = 400 \\
a_{20} - a_{15} &= 1400 - 1000 = 400 \\
a_{25} - a_{20} &= 1800 - 1400 = 400 \\
a_{30} - a_{25} &= 2400 - 1800 = 600 \\
a_{35} - a_{30} &= 3000 - 2400 = 600 \\
a_{40} - a_{35} &= 3600 - 3000 = 600 \\
a_{45} - a_{40} &= 4400 - 3600 = 800 \\
a_{50} - a_{45} &= 5200 - 4400 = 800 \\
a_{55} - a_{50} &= 6000 - 5200 = 800 \\
a_{60} - a_{55} &= 6800 - 6000 = 800 \\
a_{65} - a_{60} &= 7800 - 6800 = 1000 \\
a_{70} - a_{65} &= 8600 - 7800 = 800 \\
a_{75} - a_{70} &= 9800 - 8600 = 1200 \\
a_{80} - a_{75} &= 10800 - 9800 = 1000 \\
a_{85} - a_{80} &= 12800 - 10800 = 2000 \\
a_{90} - a_{85} &= 13200 - 12800 = 400 \\
a_{95} - a_{90} &= 14600 - 13200 = 1400 \\
a_{100} - a_{95} &= 15800 - 14600 = 1200 \\
a_{105} - a_{100} &= 17000 - 15800 = 1200 \\
a_{110} - a_{105} &= 18400 - 17000 = 1400 \\
a_{115} - a_{110} &= 19800 - 18400 = 1400 \\
a_{120} - a_{115} &= 21400 - 19800 = 1600 \\
a_{125} - a_{120} &= 23000 - 21400 = 1600 \\
a_{130} - a_{125} &= 24600 - 23000 = 1600 \\
a_{135} - a_{130} &= 26200 - 24600 = 1600 \\
a_{140} - a_{135} &= 27800 - 26200 = 1600 \\
a_{145} - a_{140} &= 29600 - 27800 = 1800 \\
a_{150} - a_{145} &= 31400 - 29600 = 1800 \\
\end{align*}
\]

Observamos que las diferencias no son constantes, lo que sugiere que no es una progresión aritmética simple. Sin embargo, parece que hay incrementos que aumentan gradualmente y, en algunos casos, se repiten.

Para simplificar, podemos establecer que los términos faltantes incrementan en pasos que siguen el patrón observado en las diferencias calculadas. Con este patrón, rellenamos los valores faltantes basándonos en las diferencias aproximadas:

\[
\begin{align*}
a_5 &= 400 + 200 = 600 \\
a_6 &= 600 + 200 = 800 \\
a_7 &= 800 + 200 = 1000 \\
a_8 &= 1000 + 200 = 1200 \\
a_9 &= 1200 + 200 = 1400 \\
a_{11} &= 600 + 200 = 800 \\
a_{12} &= 800 + 200 = 1000 \\
a_{13} &= 1000 + 200 = 1200 \\
a_{14} &= 1200 + 200 = 1400 \\
a_{16} &= 1000 + 200 = 1200 \\
a_{17} &= 1200 + 200 = 1400 \\
a_{18} &= 1400 + 200 = 1600 \\
a_{19} &= 1600 + 200 = 1800 \\
a_{21} &= 1400 + 200 = 1600 \\
a_{22} &= 1600 + 200 = 1800 \\
a_{23} &= 1800 + 200 = 2000 \\
a_{24} &= 2000 + 200 = 2200 \\
a_{26} &= 2400 + 200 = 2600 \\
a_{27} &= 2600 + 200 = 2800 \\
a_{28} &= 2800 + 200 = 3000 \\
a_{29} &= 3000 + 200 = 3200 \\
a_{31} &= 3600 + 200 = 3800 \\
a_{32} &= 3800 + 200 = 4000 \\
a_{33} &= 4000 + 200 = 4200 \\
a_{34} &= 4200 + 200 = 4400 \\
a_{36} &= 4400 + 200 = 4600 \\
a_{37} &= 4600 + 200 = 4800 \\
a_{38} &= 4800 + 200 = 5000 \\
a_{39} &= 5000 + 200 = 5200 \\
a_{41} &= 6000 + 200 = 6200 \\
a_{42} &= 6200 + 200 = 6400 \\
a_{43} &= 6400 + 200 = 6600 \\
a_{44} &= 6600 + 200 = 6800 \\
a_{46} &= 6800 + 200 = 7000 \\
a_{47} &= 7000 + 200 = 7200 \\
a_{48} &= 7200 + 200 = 7400 \\
a_{49} &= 7400 + 200 = 7600 \\
a_{51} &= 7800 + 200 = 8000 \\
a_{52} &= 8000 + 200 = 8200 \\
a_{53} &= 8200 + 200 = 8400 \\
a_{54} &= 8400 + 200 = 8600 \\
a_{56} &= 8600 + 200 = 8800 \\
a_{57} &= 8800 + 200 = 9000 \\
a_{58} &= 9000 + 200 = 9200 \\
a_{59} &= 9200 + 200 = 9400 \\
a_{61} &= 9400 + 200 = 9600 \\
a_{62} &= 9600 + 200 = 9800 \\
a_{63} &= 9800 + 200 = 10000 \\
a_{64} &= 10000 + 200 = 10200 \\
a_{66} &= 10200 + 200 = 10400 \\
a_{67} &= 10400 + 200 = 10600 \\
a_{68} &= 

Explore how to calculate missing values in an arithmetic sequence with given terms, including detailed step-by-step solutions and pattern recognition. This problem involves identifying incremental patterns and applying them systematically. Suitable for advanced mathematics enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation