# CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 10**:

A ladder has rungs apart (see figure) . The rungs decrease uniformly in length from 45 cm, at the bottom to at the top. If the top and the bottom rungs are apart, what is the length of the wood required for the rungs?

**Answer**:

Number of rungs

The length of the wood required for rungs sum of rungs

**Question 11**:

The houses of a row are numbered consecutively from to . Show that there is a value of such that the sum of the numbers of the houses preceding the house numbered is equal to the sum of the numbers of the houses following it. Find this value of

**Answer**:

Here and

According to question,

Since is a counting number, so negative value will be neglected.

**Question 12**:

Find the first term and the common difference

**Answer**:

**Question 13**:

Is Form an AP?

**Answer**:

d_1 ⧵ne d_2

Hence, it is not an AP.