Sequences

Step 1: Use the formula for harmonic progression.
For a harmonic progression, the terms are the reciprocals of the terms of an arithmetic progression. Using the given terms, we can find the common difference of the arithmetic progression.
Step 2: Find .
By applying the formula for the harmonic progression, we find:
Step 3: Conclusion.
Thus, , corresponding to option (C).

Step 1: Use the formula for sum of squares.
The formula for the sum of squares of the first natural numbers is:
Step 2: Find the sum of squares from to .

Step 3: Subtract the unwanted terms.
We need the sum from to , so subtract:
Step 4: Final calculation.
Final Answer:

Step 1: Write the given formula.
The sum of the first terms is given as

Step 2: Find the fourth term using .


Step 3: Compute the fourth term.


Step 4: Conclusion.
The fourth term of the sequence is