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Find the formula for the nth term of these sequences:

(a) 2, 5, 10, 17, 26, …….

(b) 4, 10, 20, 34, 52, ………

Part of a geometric sequence is given below:

,,,,, -1, ,,,, , ,,,,,, 64, ,,,,,

Where uₙ means the nth term, hence, u₂ = -1, and u₅ = 64.

Second term is -1, and the fifth term is 64. Calculate:

(a) The common ratio (r)

(b) The value of the first term (a) or u₁

(c) The value of the 10th term.

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A child makes a pitcher of fruit punch by completely dissolving fruit- flavoured powder in water. The child drinks a glass and decides the punch needs to be sweeter, so she stirs in more powder. This time the powder does not all dissolve, but settles on the bottom of the pitcher. A) Is the fruit-flavoured powder a pure substance or a mixture? * helpme anyone?

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