In an AP, if a = 3.5, d = 0, n = 101, then aₙ will be
a. 0
b. 3.5
c. 103.5
d. 104.5

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Considering the question, we get the value as,

aₙ = 3.5 + (101 - 1) × 0

aₙ = 3.5 + (100) × 0

aₙ = 3.5.

Therefore, aₙ = 3.5.

✦ Try This: If the 5th term of an AP is 40 with a common difference of 6. Find out the arithmetic progression

It is given that

T5 = 40

d = 6

We can write the fifth term as

T5 = a + (5 - 1) 6

T5 = a + 24

Here

a + 24 = 40

a = 40 - 24

a = 16

So the arithmetic progression is

T1 = a = 16

T2 = a + d

T2 = 16 + 6 = 22

T3 = a + 2d

T3 = 16 + 2 (6) = 16 + 12 = 28

T4 = a + 3d

T4 = 16 + 3(6) = 16 + 18 = 34

T5 = a + 4d

T5 = 16 + 4(6) = 16 + 24 = 40

T6 = a + 5d

T6 = 16 + 5 (6) = 16 + 30 = 46

Therefore, the arithmetic progression is 16, 22, 28, 34, 40, 46, …..

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.1 Problem 2

In an AP, if a = 3.5, d = 0, n = 101, then aₙ will be, a. 0, b. 3.5, c. 103.5, d. 104.5

Summary:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. In an AP, if a = 3.5, d = 0, n = 101, then aₙ will be 3.5

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☛ Related Questions:

• The list of numbers - 10, - 6, - 2, 2,... is, a. an AP with d = - 16, b. an AP with d = 4, c. an AP . . . .
• The 11th term of the AP: -5, -5 /2 , 0, 5/ 2 , ...is, a. -20, b. 20, c. -30, d. 30
• The first four terms of an AP, whose first term is -2 and the common difference is -2, are, a. - 2, . . . .