Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
7, 12, 17
Find the 34th term

Answer 1

The 34th term of the sequence is 172

Arithmetic sequence

This is a type of sequence which have a common difference (d) between each term

How to determine the 34th term of the sequence

From the question given above, the following data were:

• Sequence => 7, 12, 17

• First term (a) = 7

• Common difference (d) = 12 – 7 = 5

• 34th term (T₃₄) =?

T₃₄ = a + 33d

T₃₄ = 7 + (33×5)

T₃₄ = 7 + 165

T₃₄ = 172

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Answer 2

The 34th term of the sequence is 172

Sequence and series

Given the sequence 7, 12, 17...

The nth term of the sequence is expressed as;

• Tn = a + (n-1)d

Given the following

a = 7

d = 12 - 7 = 5

n = 34

Substitute the given parameters

T34 = 7 + (34 - 1)*5

T34 = 7 + (33)*5

T34 = 172

Hence the 34th term of the sequence is 172

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