# Math՚S Arithmetic Progression Questions and Answers with Solution Sample Paper

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## Arithmetic Progression

**Basic terms used**

Consider the following list of numbers

i. 1,2, 3,4 …

ii. 100, 70,40, 10 …

Each of the number in the list is called a **term**.

Let us denote the first term of an A. P. by , second term by and n^{th} term by and the common difference by d. then the A. P. becomes

So,

**term of an A. P**.

The term of an A. P. with first term a and common difference d is given by

**Sum of first n terms of an A. P**.

**Q1**. For an A. P: 3, 5, 7, 9, 11,13, 15 … Write the first term a and common difference d.

**Ans**. Here,

**Q2**. Find 10^{th}_{term} of an A. P: 2,7, 12 …

**Solution**: here,

**Q3**. Determine the A. P. whose 3^{rd} term is 5 and 7^{th} term is 9.

**Solution**: we have

(1)

(2)

Solving the pair of linear equation

Hence the required A. P. is 3, 4,5, 6,7 …

**Q4**. Find the sum of first 22 terms of an A. P: 8,3, -2 …

**Solution**: Here,

We know that

S =

**Q5**. How many terms of an A. P: 24,21, 18 … must be taken so that their sum is 78?

**Solution**:

Here,

We know that

Both values of n are admissible. So, the number of terms is either 4 or 13.