Question

ayuda porfavor con estos problemas.

Answer 1

Progresion aritmetica

an = a1 + (n - 1)d

d = a2 - a1

a) 3, 8, 13, 18, 23

a1 = 3;  d = 8 - 3 = 5; n = 258

a258 = 3 + (258 - 1)(5)

a258 = 3 + (257)(5)

a258 = 1288

b) 4, 10, 16, 22, 28, ...

a1 = 4; d = 10 - 4 = 6;  n = 258

a258 = 4 + (258 - 1)(6)

a258 = 4 + (257)(6)

a258 = 1546

c) 6, 9, 12, 15, 18, 21,...

a1 = 6; d = 9 - 6 = 3; n = 258

a258 = 6 + (258 - 1)(6)

a258 = 6 + (257)(6)

a258 = 1548

2) Sn = [(a1 + an)*n]/2

Sn = Suma de terminos

a) 5, 12, 19, 26, 33,...

Primero tenemo que hallar el termino 170

a1 = 5; d = 12 - 5 = 7; n = 170

a170 = 5 + (170 - 1)(7)

a170 = 5 + (169)(7)

a170 = 1188

Ahora si aplico Sn = [(a1 + an)*n]/2

S170 = [(5 + 1188)*170]/2

S170 = [(1193)*170]/2

S170 = [202810]/2

S170 = 101405

b) 2, 11, 20, 29, 38, ...

Primero hallamos a170

a1 = 2; d = 11 - 2 = 9;  n = 170

a170 = 2 + (170 - 1)(9)

a170 = 2 + (169)(9)

a170 = 1523

Ahora si aplico Sn = [(a1 + an)*n]/2

S170 = [(2 + 1523)*170]/2

S170 = [(1525)*170]/2

S170 = [259250]/2

S170 = 129625

c) 10, 15, 20, 25, 30, ...

a1 = 10; d = 15 - 10 = 5; n = 170

a170 = 10 + (170 - 1)(5)

a170 = 10 + (169)(5)

a170 = 855

Ahora si aplico Sn = [(a1 + an)*n]/2

S170 = [(10 + 855]*170]/2

S170 = [(865)*170]/2

S170 = [147050]/2

S170 = 73525