The nth term of a sequence is 8(2^n + 2^(6n-7)). a) Without a calculator, find the 2nd term of this sequence, b) Express the formula in the form 2^x + 2^y
To find a) just plug in the number two to all places where n appears. In this case 8(2^2 + 2^(6 * 2 - 7)) and then number crunch. 8(4+2^5) -> 8 * (4 + 32) -> 8 * 36= 288.
To find part b, we must first expand the brackets to give us 8 * 2^n + 8 * 2^(6n-7). We must then express 8 as an exponent of 2 (2^3), giving us 2^3 * 2^n + 2^3 * 2^(6n-7). This allows us to use our indices laws for multiplication, where a^n * a^m = a^(n + m). Therefore giving us 2^(n+3) + 2^(6n-4) which is the correct form.
TP
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