The first picture is got by removing the small triangle formed by joining the midpoints of an equilateral triangle. The second picture is got by removing such a middle triangle from each of the red triangles of the first picture. The third picture shows the same thing done on the second.

How many red triangles are there in each picture?

The first picture is got by removing the small triangle formed by joining the midpoints of an equilateral triangle. The second picture is got by removing such a middle triangle from each of the red triangles of the first picture. The third picture shows the same thing done on the second.

Taking the area of the original uncut triangle as $1$, compute the area of a small triangle in each picture.

The first picture is got by removing the small triangle formed by joining the midpoints of an equilateral triangle. The second picture is got by removing such a middle triangle from each of the red triangles of the first picture. The third picture shows the same thing done on the second.

What is the total area of all the red triangles in each picture?

The first picture is got by removing the small triangle formed by joining the midpoints of an equilateral triangle. The second picture is got by removing such a middle triangle from each of the red triangles of the first picture. The third picture shows the same thing done on the second.

Write the algebraic expressions for the below three sequences.

$3, 9, 27, ......$

$\frac{1}{4}, \frac{1}{16}, .....$

$3\times \frac{1}{4}, 9\times \frac{1}{16}, 27\times \frac{1}{64}, ........$

Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of odd numbers.

Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of even numbers.

Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of fractions got as half the odd numbers.

Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of powers of $2$.

Check whether the sequence given below is an arithmetic sequence. Give reasons. For the arithmetic sequences, write the common difference also.

Sequence of reciprocals of natural numbers.