Question

Consider the arithmetic sequence is 1,4,7.... what is its 21st term.​

Answer 1

Answer:

The 21ˢᵗ term of the given AP is 61.

Step-by-step-explanation:

The given arithmetic progression is 1, 4, 7,....

• a = t₁ = 1
• d = t₂ - t₁ = 4 - 1 = 3

We have to find the 21ˢᵗ term of this AP.

We know that,

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

⇒ t₂₁ = 1 + ( 21 - 1 ) * 3

⇒ t₂₁ = 1 + 20 * 3

⇒ t₂₁ = 1 + 60

⇒ t₂₁ = 61

∴ The 21ˢᵗ term of the given AP is 61.

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Additional Information:

1. Arithmetic Progression:

In a sequence of numbers, if the difference between two consecutive terms is constant, then the sequence is called Arithmetic Progression or AP.

2. nᵗʰ term of AP:

The nᵗʰ term of the AP is the term at nᵗʰ place in the sequence.

3. Formula for nᵗʰ term of AP:

• tₙ = a + ( n - 1 ) * d

Where,

• tₙ = nᵗʰ term of AP
• a = First term of AP
• n = Number of terms in AP
• d = Common difference of AP ( t₂ - t₁ )

4. Sum of first n terms of AP:

The sum of the n number of terms in an AP is the sum of n terms of AP.

5. Formula for sum of n terms of AP:

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

Where,

• Sₙ = Sum of first n number of terms
• n = Number of terms in AP
• a = First term of AP
• d = Common difference of AP