Problem:If the 13th, 14th and 15th terms of an arithmetic sequence are 18, 21, 24 respectively, what is the 19th term?
Solution:Write the given sequence.
- d_13 = 18
- d_14 = 21
- d_15 = 24
Find the common difference.
- d = a_14 - a_13
- d = 21 - 18
- d = 3
- d = a_15 - a_14
- d = 24 - 21
- d = 3
So, the common difference is 3.
To find the 19th term add the common difference to the preceding term to get the next terms.
- a_13 = 18
- a_14 = 18 + 3 = 21
- a_15 = 21 + 3 = 24
- a_16 = 24 + 3 = 27
- a_17 = 27 + 3 = 30
- a_18 = 30 + 3 = 33
- a_19 = 33 + 3 = 36
Answer:∴ Therefore, the 19th term of the arithmetic sequence is 36.
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