Question

2. Find the sum of the arithmetic series 3+7+11+.....upto 35
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Answer 1

Answer:

The sum of the numbers upto 35 of the given arithmetic series is 171.

Step-by-step-explanation:

We have given that,

3, 7, 11,......, 35 is an Arithmetic Progression.

Here,

First term ( t₁ ) = a = 3

Common difference = d

d = t₂ - t₁

⇒ d = 7 - 3

⇒ d = 4

We have to find the sum upto 35.

∴ Last term ( tₙ ) = 35

Now, we know that,

tₙ = a + ( n - 1 ) * d - - [ Formula ]

⇒ 35 = 3 + ( n - 1 ) * 4

⇒ 35 - 3 = ( n - 1 ) * 4

⇒ 32 = ( n - 1 ) * 4

⇒ n - 1 = 32 ÷ 4

⇒ n - 1 = 8

⇒ n = 8 + 1

⇒ n = 9

Now, we know that,

Sₙ = ( n / 2 ) [ a + l ] - - [ Formula ]

⇒ S₉ = ( 9 / 2 ) [ 3 + 35 ]

⇒ S₉ = 9 / 2 × 38

⇒ S₉ = 9 × 38 ÷ 2

⇒ S₉ = 9 × 19

⇒ S₉ = 171

∴ The sum of the numbers upto 35 of the given arithmetic series is 171.

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Additional Information:

1. Arithmetic Progression:

1. In a sequence, if the common difference between two consecutive terms is constant, then the sequence is called as Arithmetic Progression ( AP ).

2. nᵗʰ term of an AP:

The number of a term in the given AP is called as nᵗʰ term of an AP.

3. Formula for nᵗʰ term of an AP:

• tₙ = a + ( n - 1 ) * d

4. The sum of the first n terms of an AP:

The addition of either all the terms of a particular terms is called as sum of first n terms of AP.

5. Formula for sum of the first n terms of A. P. :

• Sₙ = ( n / 2 ) [ 2a + ( n - 1 ) * d ]