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.

Answer 1

First term of the sequence is 10 and common difference is 3.
$a_1$ = 10 and d = 3
Next term = $a_2=a_1+d=10+3=13$
$a_3=a_2+d=13+3=16$
Thus, first three terms of the sequence are 10, 13 and 16.
Let 100 be the nth term of the sequence.
$a_n=a_1+(n-1)d$
$100=10+(n-1)3$
$90=(n-1)3$
$n-1=30$
$n=31$, which is a whole number.
Therefore, 100 is the ${31}^{st}$ term of the sequence.