# 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.