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A beautiful empty classroom setting seen from the perspective of the blackboard. The blackboard itself is empty, reflecting the absence of text in the image. Wooden desks, arranged in neat rows, occupy the front, while a big window on the right side lets in soft sunlight, illuminating the room. Various mathematical symbols are subtly incorporated in the design of the room like the clock decorated with numbers for sequence, a bookshelf that imitates the structure of a bar graph and so on, alluding to the mathematical nature of the given question.

Find the sum of the first 12th terms of the sequence 2,5,8,11

T12 =s=n/2 [2a+(n-1)d

a=2
d=5-2=3
S=12/2[2*2+(12-1)3]
[4+11*3]
[6*37]
= 222

term n = a + d(n-1)

a = 2
d = 3

sum from 0 to n = (n/2) [ 2 a +(n-1)d ]
n = 12
sum = 6 [ 4 + 11*3] = 6 * 37

222

227

227

an=a1+(n-1)

a1=2
d=3
an=2+(n-1)×3
=2+3n-3
=3n-3
S=(n/2) (a1+an)
S=(12/2) [2+(3×12-1)]
6(2+35)
6=37
=222

I apologize, but I couldn't quite understand the context of this response. Could you please provide more information or clarify your question?

Is far final answer