If for some number a and d,if first term is 1⁄a, second term is 1/(a+d) ,thrid term is 1/(a+2d) and so on, then 5th term of the sequence is :________?
I am attempting to answer the question above. I assumed that I would just add a 'd' for every term, so I did the following:
First term: $\frac{1}{a}$
Second term: $\frac{1}{a+d}$
Third term: $\frac{1}{a+2d}$
Fourth term: $\frac{1}{a+3d}$
Fifth term: $\frac{1}{a+4d}$
My answer is $\frac{1}{a+4d}$; however, I worry that merely adding a 'd' might be wrong.
You cannot (uniquely) answer the question from the given information.
If the sequence is the sequence $(x_n)_n$ defined by $x_n=\frac 1 {a+(n-1)d}$, then the fifth term is as you said.
However, there are infinitelymany sequences starting with the first four terms as given.
You could simply take your favorite sequence and replace the first four terms, for example take a constant sequence:
$x_0= \frac 1 a$, $x_1= \frac 1 {a+d}$, ..., $x_4= \frac 1 {a +3d}$, $x_5= 0$, $x_6=0$, $x_n=0$ for $n>4$