Which is the last number in the `30^(th)` row?

. Which is the first number in the 30^(th) row?

Consider the numbers between 100 and 300 which leave remainder 2 on division by 3 a) Which is the first number in this sequençe? b) Which is the last number in this sequence? c). How many such numbers are there in this sequence? d) Find the, sum of all numbers in the sequence.

Observe the number pattern made using terms of an arithmetic sequence 2, 6,10, ... . Find the first and the last numbers in the 20th line.

Write the first and the last numbers of the 10^(th) line.

Observe the number pattern made using terms of an arithmetic sequence 2, 6,10, ... . Which term of the arithmetic sequence 2, 6,10, ... is the last number of the 20th row of the above pattern.

. What is the sum of all terms in the first 30 rows ?

Observe the following pattern of dots i) Find the number of dots in the n^(th) pattern. ii) Find the sum of number of dots upto n^(th) pattern and the mathematical statement using these facts. iii)Prove the statement obtained in question (ii) using principle of mathematical induction.

. How many numbers are there in the 30^(th) row of this number pyramid?