Question

1.Find the 6th term from the end of the A.P 17, 14, 11, …………. – 40?

2.The sum of the 4th term and 8th term of as A.P is 24 and the sum of the 6th term and 10th term is 44. Find the first three terms of the A.P?

Answer 1

Answer:

$\huge\sf\red{AɴsᴡEʀ \: 1}$

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◆ Given,

Hence, the 6th term from the end is –25.

$\huge\sf\purple{AɴsᴡEʀ \: 2}$

The formula for nth term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the nth term, a is the first term, d is the common difference and n is the number of terms.

Given, a₄ + a₈ = 24

(a + 3d) + (a + 7d) = 24

⇒ 2a + 10d = 24

⇒ a + 5d = 12 Equation(1)

Also, a₆ + a₁₀ = 44

(a + 5d ) + (a + 9d) = 44

⇒ 2a + 14d = 44

⇒ a + 7d = 22 .... Equation(2)

On subtracting equation (1) from (2), we obtain

(a + 7d ) - (a + 5d) = 22 - 12

a + 7d - a - 5d = 10

2d = 10

d = 5

By substituting the value of d = 5 in equation (1), we obtain

a + 5d = 12

a + 5 × 5 = 12

a + 25 = 12

a = - 13

The first three terms are a , (a + d) and (a + 2d)

Substituting the values of a and d , we get - 13, (- 13 + 5) and (- 13 + 2 × 5)

The first three terms of this A.P. are - 13, - 8, and - 3.

Answer 2

Answer:

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