Kerala Board Solutions for Chapter: Arithmetic Sequences, Exercise 3: Exercise 3

Write the algebraic expression for the sequence below:

Sequence of natural numbers which leave remainder $1$ on division by $3$.

Write the algebraic expression for the sequence below:

The sequence of natural numbers ending in $1$.

Write the algebraic expression for the sequence below:

The sequence of natural numbers ending in $1$ or $6$.

For the sequence of regular polygons starting with an equilateral triangle, write the algebraic expressions for the sequence of the sums of inner angles, the sums of the outer angles, the measures of an inner angle, and the measure of an outer angle.

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.

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

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

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