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Question

First term of an arithmetic sequence is 10 and its common difference 3. Write the first three terms of the sequence. Verify whether 100 is a term of this sequence.

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Solution

First term of the sequence is 10 and common difference is 3.
a1 = 10 and d = 3
Next term = a2=a1+d=10+3=13
a3=a2+d=13+3=16
Thus, first three terms of the sequence are 10, 13 and 16.
Let 100 be the nth term of the sequence.
an=a1+(n1)d
100=10+(n1)3
90=(n1)3
n1=30
n=31, which is a whole number.
Therefore, 100 is the 31st term of the sequence.

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