Question

The first three terms of an arithmetic sequence are 2k-7; k+8 and 2k-1.
Calculate the value of the 15th term of the sequence.
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Answer 1

Answer:

Use the definition of an arithmetic sequence to set up a system of two equations and two unknowns and solve.

Explanation:

Since the sequence is arithmetic, there is a number d (the common difference) with the property 5k-2= (2k+3) +d and 10k-15=(5k-2)+d. The first equation can be simplified to 3k-d=5 and the second to 5k-d=13. You can now subtract the first of these last two equations from the second to get 2k=8, implying that k=4.

Alternatively, you could have set d=3k-5= 5k-13 and solved for k=4 that way instead of substracting one equation from the other

It's not necessary to find, but the common difference d=3k-5=3.4-5=7

the three terms in the sequence are 11,18,25