Find n, the number of terms:
a₁ = 2
an = 100
d = 2
an = a₁ + (n-1)(d)
100 = 2 + (n-1)(2)
100/2 = 2n/2
n = 50
Find the sum of the sequence:
Sn = n/2 {a₁ + an)
S₁₀₀ = 50/2 (2 + 100)
S₁₀₀ = 25 (102)
To find the rule of the given sequence:
an = 2 + (n-1)(2)
an = 2 - 2 + 2n
an = 2n ⇒ the nth rule/pattern of the given sequence.