Two APs have the same common difference. The first term of one of these is -1 and that of the other is - 8. Then the difference between their 4th terms is
a. -1
b. - 8
c. 7
d. -9

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.

Let the common difference be d₁ and d₂.

By the condition given,

d₁ = d₂ = d----------------------------------------------- (i)

The first term of the first AP be (a₁) = -1

The first term of the second AP be (a₂) = -8.

4th term of first AP,

T₄ = a₁ + (4 - 1)d

T₄ = -1 + 3d.

4th term of second AP,

T₄‘ = a₂ + (4 - 1)d

T₄‘ = -8 + 3d.

The difference between their 4th terms is

꘡T₄ - T₄’꘡= (-1 + 3d) - (-8 + 3d)

꘡T₄ - T₄’꘡= -1 + 3d + 8 - 3d = 7

꘡T₄ - T₄’꘡= 7.

Therefore, the required difference is 7.

✦ Try This: In an AP, the sum of the first 3 terms is - 60 and that of the last 3 are 84. If there are 15 terms, what is the sum of the middle 3 terms

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

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NCERT Exemplar Class 10 Maths Exercise 5.1 Problem 11

Two APs have the same common difference. The first term of one of these is -1 and that of the other is - 8. Then the difference between their 4th terms is, a. -1, b. - 8, c. 7, d. -9

Summary:

Two APs have the same common difference. The first term of one of these is -1 and that of the other is - 8. Then the difference between their 4th terms is 7

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☛ Related Questions:

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• The 4th term from the end of the AP: -11, -8, -5, ...,49 is, a. 37, b. 40, c. 43, d. 58
• The famous mathematician associated with finding the sum of the first 100 natural numbers is, a. Pyt . . . .