Question

Find the 13th term of the sequence 8, -16, 32, -64

Answer 1

try to see the pattern, first start by the numbers regardelss of the signs: 2, 16, 32, 64.. what does it tell you: they are the powers of 2: 2^3 =8, 2^4=16, 2^6=64.. now try to figure out the signs, when the power is even the expressions become negative. A convenient way to do it is: -((-2)^n): when you plug any odd number you get a positive result, while you get negative results when you plug any even number. Now, the first term is -(-2)^3) = 8 so the 13th term would be -(-2)^16) = -65536