Finding the Values of a and d (Leaving Cert Mathematics): Quizzes

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Finding the Values of a and d
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In the general term formula Tn=a+(n−1)dT_n = a + (n-1)d, what does aa represent?

The first term of the sequence

When given two terms of an arithmetic sequence, what is the key strategy for finding aa and dd?

Create two equations with two unknowns

When solving simultaneous equations to find aa and dd, which should you find first?

Find dd first

For consecutive terms in an arithmetic sequence, what property must hold true?

The common difference must be the same

In Example 1, given T4=11T_4 = 11 and T9=21T_9 = 21, what is the value of dd?

d=2d = 2

In Example 1 with a=5a = 5 and d=2d = 2, what is T50T_{50}?

T50=103T_{50} = 103

In Example 2, if x+1x+1, 2x−22x-2, 2x+12x+1 are consecutive terms, what is the value of xx?

x=6x = 6

In Example 2 with x=6x = 6, what is the general term TnT_n of the sequence?

Tn=3n+4T_n = 3n + 4

In Example 2 with Tn=3n+4T_n = 3n + 4, what is T100T_{100}?

T100=304T_{100} = 304

In Example 3, given T5=21T_5 = 21 and T10=41T_{10} = 41, what is the value of dd?

d=4d = 4

What should you do to check your answer after finding aa and dd?

Substitute back into original terms

What is a common mistake when using the general term formula Tn=a+(n−1)dT_n = a + (n-1)d?

Forgetting the (n−1)(n-1)

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