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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

The common difference (d) can be found by subtracting the first term from the second term:

$d = 7 - 3 = 4$

Step 2

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Answer

The first term (a) of the sequence is:

$a = 3$

Step 3

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Answer

The formula for the nth term of an arithmetic sequence is given by:

$t_n = a + (n - 1)\cdot d$

For the 15th term:

$t_{15} = a + (15 - 1)\cdot d = 3 + 14 \cdot 4$

Calculating this gives:

$t_{15} = 3 + 56 = 59$

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