Bunuel wrote:

If S is the infinite sequence such that \(t_1 = 4\), \(t_2 = 10\), …, \(t_n = t_{n-1} + 6\),…, what is the sum of all the terms from \(t_{10}\) to \(t_{18}\)?

(A) 671

(B) 711

(C) 738

(D) 826

(E) 991

As there are specific rules for straightforward calculation of sums of arithmetic sequences, we'll use them.

This is a Precise approach.

To calculate the sum of an arithmetic sequence, we need to know the first number, the last number and the number of elements in the sequence.

Our first number is t_10 which is equal to t_1 + d*9 = 4 + 6*9 = 58.

Our last number is t_18 which is equal to t_10 + d*8 = 58 + 6*8 = 106

As there are 9 total elements, our sum is (58+106)*9/2 = 164*9/2 = 82*9 = 82(10 - 1) = 820-82 = 738

(C) is our answer.

Note that as all elements of our sequence are even, we could also have eliminated (A), (B), (E) without calculation and then guessed bewteen (C) and (D).

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