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Given the arithmetic sequence that starts

−8, 10, . . .
(a) Find the 20th term of the sequence. (Given that −8 is the first term.)
(b) Find the sum of the first 37 terms of the sequence

the difference (between terms) is ... 10 - -8 = 18

(a) -8 + (19 * 18) = ?

(b) the 37th term is ... -8 + (36 * 18) = ?
... the sum is ... [-8 + (37th term)] * (37/2)

Did you know?

Did you know that an arithmetic sequence is a sequence in which the difference between any two consecutive terms is always the same? For example, if a sequence starts with -8 and the second term is 10, the common difference is 10 - (-8) = 18. Now, did you know that to find the 20th term of an arithmetic sequence, we can use the formula: term = first term + (n - 1) * common difference? In this case, the first term is -8, the common difference is 18, and the value of n (which represents the term number) is 20. Plugging these values into the formula, we get: term = -8 + (20 - 1) * 18 = -8 + 19 * 18 = -8 + 342 = 334. So, the 20th term of this sequence is 334. Moreover, did you know that to find the sum of the first n terms of an arithmetic sequence, we can use the formula: sum = (n/2) * (first term + last term)? In this case, the first term is -8, the common difference is 18, and the value of n is 37. To find the last term, we can use the same formula as before: last term = -8 + (37 - 1) * 18 = -8 + 36 * 18 = -8 + 648 = 640. Plugging these values into the sum formula, we get: sum = (37/2) * (-8 + 640) = 18.5 * 632 = 11704. So, the sum of the first 37 terms of this sequence is 11704.