Sum of the sequence 33+34+35+36+...+122

Question

I've been trying to do this pattern for 4 days now. I've even went through and plugged in every number separately and I still can't get the answer. Please help!

Answer 1

First determine the number of terms

 

a_n = a₁ + (n - 1)d, where a₁ = first term, d = common difference, n = number of terms

122 = 33+ (n - 1)1

122 = 33 + n = 1

122 = 32 + n

90 = n

 

Now determine the sum

 

S_n = n/2 (a₁ + a_n)

S₉₀ = 90/2 (33 + 122)

S₉₀ = 45(155)

S₉₀ = 6975