Question

Hitunglah! (a) 1+2+3+4...+100=..
(b) 67+68+69+70+71+72+73=..

Answer 1

A) suku awal = a = 1
    beda = b = 1
 
Un = a +(n-1)b
Un = 1 +(n-1)1
Un = 1 + 1n - 1
Un = 1n

100 = 1n
n = 100/1
n = 1

Sn = n/2 (a+Un)
S100 = 100/2 (1+100)
S100 = 50 (101) = 5050

b) suku awal = a = 67
    beda = b = 1

Un = a +(n-1)b
Un = 67 +(n-1)1
Un = 67 + 1n - 1
Un = 66 + n

73 = 66 + n
n = 73 - 66
n = 7

Sn = n/2 (a+Un)
S7 = 7/2 (67 + 73)
S7 = 3,5 (140) = 490
 

Answer 2

(a) a = 1, b = 1
 Un = a +  b(n - 1)
100 = 1 + 1 (n - 1)
100 = 1 + n - 1
-n = 1 - 1 - 100
n = 100

Sn = 1/2 n (2a + b (n - 1)) 
S₁₀₀ = 1/2 (100) (2(1) + 1 (100 - 1))
S₁₀₀ = 50 (2 + 99)
S₁₀₀ = 50 x 101 = 5050

(b) 67 + 68 + 69 + 70 + 71 + 72 + 73 =  490