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The first three terms of an arithmetic sequence are 3, 7 and 11 - HSC - SSCE Mathematics Advanced - Question 11 - 2023 - Paper 1

Question 11

The first three terms of an arithmetic sequence are 3, 7 and 11. Find the 15th term.

Worked Solution & Example Answer:The first three terms of an arithmetic sequence are 3, 7 and 11 - HSC - SSCE Mathematics Advanced - Question 11 - 2023 - Paper 1

Step 1

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Answer

To find the common difference, we can subtract the first term from the second term:

$d = 7 - 3 = 4$

Step 2

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Answer

The first term, denoted as 'a', is:

$a = 3$

Step 3

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Answer

Using the formula for the nth term of an arithmetic sequence: $t_n = a + (n - 1)d$ we can find the 15th term:

$t_{15} = 3 + (15 - 1) \cdot 4$

Calculating this: $t_{15} = 3 + 14 \cdot 4 = 3 + 56 = 59$

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