Question

In a sequence, the 40th term is 70, the 41st term is 72 and the 42nd term is 74.

a) State the term-to-term rule

b) Work out the first term

c) Work out the 80th term

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Answer 1

term to term rule is +2

The first term is -8

80th term is 150

Explanation:

70 to 72 is adding 2

72 to 74 is adding 2

term to term rule is +2

The equation for a sequence like this is

xn = a + d(n−1)

where n is the term number a is the first term and d is the term to term rule

Using the 40th term is 70

70 = a + 2( 40-1)

70 = a + 2( 39)

70 = a + 78

Subtract 78 from each side

-8 = a

The first term is -8

80th term

xn = a + d(n−1)

x80 = -8 +2 (80-1)

= -8+2(79)

= -8+158

= 150