Find the next two terms in the following sequence:
13, -5, -35, -77,...
Answer (2)
13 ; − 5 ; − 35 ; − 77 ; ... a n = 19 − 6 n 2 a 1 = 19 − 6 ⋅ 1 2 = 19 − 6 = 13 a 2 = 19 − 6 ⋅ 2 2 = 19 − 6 ⋅ 4 = 19 − 24 = − 5 a 3 = 19 − 6 ⋅ 3 2 = 19 − 6 ⋅ 9 = 19 − 54 = − 35 a 4 = 19 − 6 ⋅ 4 2 = 19 − 6 ⋅ 16 = 19 − 96 = − 77 a 5 = 19 − 6 ⋅ 5 2 = 19 − 6 ⋅ 25 = 19 − 150 = − 131 a 6 = 19 − 6 ⋅ 6 2 = 19 − 6 ⋅ 36 = 19 − 216 = − 197
The next two terms in the sequence 13, -5, -35, -77,... are -55 and -102, derived from the quadratic formula a n = − 6 n 2 + 19 n . Following the sequence's established pattern allowed for these terms to be calculated accurately.
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