Question

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CLASS 10TH
ARITHMETIC PROGRESSIONS​

Answer 1

Question:

The 11th term of the AP: -5, -5/2, 0, 5/2... is?

Answer:

an = a + (n-1)d

a = -5

d = -5/2 - (-5)

d = -5/2 + 5

d = 5/2

a₁₁ = -5 + (11 - 1)5/2

= -5 + 10(5/2)

= -5 + (50/2)

= -5 + 25

= 20

11th term of the given AP is 20.

_________________________

Additional info:

❇ General form of an AP:

a, a+d, a+2d..

❇ Sum of n terms is given as:

Sn = n/2(2a + (n-1)d)

❇ Sum of AP when last term is given:

S = n/2(a + l)

Answer 2

Answer:

• 11th term of AP is 20.

Step-by-step explanation:

Given:

• ${\sf{AP:\;-5,\;\dfrac{-5}{2},\;0,\;\dfrac{5}{2},....}}$
• a₁ = -5
• a₂ = -5/2

To Find:

• 11th term of AP.

Formula used:

• aₙ = a + (n - 1)d

Now, first we will find common difference.

⇒ d = a₂ - a₁

⇒ d = (-5/2) - (-5)

⇒ d = (-5 + 10)/2

⇒ d = 5/2

Now, we know that

⇒ aₙ = a + (n - 1)d

⇒ a₁₁ = a + (11 - 1)d

⇒ a₁₁ = a + 10d

⇒ a₁₁ = - 5 + 10 × 5/2

⇒ a₁₁ = - 5 + 50/2

⇒ a₁₁ = (-10 + 50)/2

⇒ a₁₁ = 40/2

⇒ a₁₁ = 20

Hence, 11th term of AP is 20.