Solving Problems Involving APs and GPs (HSC SSCE Mathematics Advanced): Quizzes

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Solving Problems Involving APs and GPs
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What condition must be satisfied for three numbers aa, bb, cc to form an AP?

ba=cbb - a = c - b

If three numbers form a GP, what relationship holds?

b2=acb^2 = ac

Find xx if 55, xx, 1515 form an AP.

x=10x = 10

If 22, xx, 88 form a GP, what are the possible values of xx?

x=4x = 4 or x=4x = -4

When solving AP simultaneous equations, which operation eliminates aa?

Subtraction

When solving GP simultaneous equations, which operation eliminates aa?

Division

If three numbers form an AP, what is the middle term?

Average of the outer two terms

Which formula gives the nnth term of a GP?

Tn=arn1T_n = ar^{n-1}

When is trial-and-error most practical for GP index problems?

Target value is relatively small

For a GP with T4=8T_4 = 8 and T6=32T_6 = 32, how do you find rr?

Divide T6T_6 equation by T4T_4 equation

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