# NCERT Class 11-Math՚s: Chapter – 9 Sequence and Series Part 9 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 6**:

We know the sum of the interior angles of a triangle is . Show that the sums of the interior angles of polygons with sides form an arithmetic progression. Find the sum of the interior angles for a sided polygon.

**Answer**:

**Question 7**:

A side of an equilateral triangle is long. A second equilateral triangle is inscribed in it by joining the mid points of the sides of the first triangle. The process is continued as shown in the accompanying diagram. Find the perimeter of the sixth inscribed equilateral triangle.

**Answer**:

**Question 8**:

In a potato race potatoes are placed in a line at intervals of metres with the first potato metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

**Answer**:

**Question 9**:

In a cricket tournament school teams participated. A sum of is to be awarded among themselves as prize money. If the last placed team is awarded in prize money and the award increases by the same amount for successive finishing places, how much amount will the first place team receive?

**Answer**:

**Question 10**:

If are in A. P. , where for all , show that

**Answer**:

To prove that:

Multiplying the first term by the second term by and so on that is rationalizing each term

Using

As are in AP let its common difference be d

Hence multiplying by -1

Put these values in LHS

Multiply divide by

Using

The term of AP is given by

Where the is the last n^{th} term and is the first term

Hence

Substitute in LHS

Hence proved