Jawaban:

1. 2+4+6+8........+100=

a = 2

b = 4 - 2 = 2

Un = a + (n-1)b

100 = 2 + (n-1)2

100-2 = (n-1)2

50 = (n-1)2

n-1 = 50:2

n-1 = 25

n = 25+1

n = 26

Sn = n/2 (2a + (n-1)b)

S26 = 26/2 (2(2) + 25(2))

= 13 (4 + 50)

= 13 (54)

= 702

2. 7+10+13+16+........+79=

a = 7

b = 10 - 7 = 3

Un = a + (n-1)b

79 = 7 + (n-1)3

79-7 = (n-1)3

72 = (n-1)3

n-1 = 72:3

n-1 = 24

n = 24+1

n = 25

Sn = n/2 (2a + (n-1)b)

S25 = 25/2 (2(7) + 24(4))

= 25/2 (14 + 96)

= 25/2 (110)

= 25 (55)

= 1375

3. 185+183+181+179+..........+87=

a = 185

b = 183 - 185 = -2

Un = a + (n-1)b

87 = 185 + (n-1)(-2)

87-185 = (n-1)(-2)

-98 = (n-1)(-2)

n-1 = -98:(-2)

n-1 = 49

n = 49+1

n = 50

Sn = n/2 (2a + (n-1)b)

S50 = 50/2 (2(185) + 49(-2))

= 25 (370 - 98)

= 25 (272)

= 6800

4. -1 + -3 + -4 + -5 + -6 + -7+.............+100=

Sepertinya soalnya ada yang kurang. Harusnya ada -2 nya dan suku terakhirnya ada tanda negatifnya menjadi -100

-1 + -2 + -3 + -4 + -5 + -6 + -7+.............+100=

a = -1

b = -2 - (-1) = -2 + 1 = -1

Un = a + (n-1)b

-100 = -1 + (n-1)(-1)

-100+1 = (n-1)(-1)

-99 = (n-1)(-1)

n-1 = -99 : (-1)

n-1 = 99

n = 99 + 1

n = 100

Sn = n/2 (2a + (n-1)b)

S100 = 100/2 (2(-1) + 99(-1))

= 50 (-2 + (-99))

= 50 (-101)

= -5050

5. 1+2+3+4+.......+2020=

a = 1

b = 2 - 1 = 1

n = 2020

Sn = n/2 (2a + (n-1)b)

S2020 = 2020/2 (2(1) + 2019(1))

= 1010 (2 + 2019)

= 1010 (2021)

= 2041210