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 nth 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 10th term of an A.P: 2, 7, 12 . . . . . . . . . .

Solution: here,

Q3. Determine the A.P. whose 3rd term is 5 and 7th 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.