Question

In an A.P first term and common difference is 3 and 5 respectively. Its 16th term is
A) 34 B] 24 J14 D] 44 ​

Answer 1

Answer:

The 16ᵗʰ term of the AP is 78.

Step-by-step-explanation:

We have given that,

For an AP

• First term ( a ) = 3
• Common difference ( d ) = 5

We have to find the 16ᵗʰ term of the AP.

We know that, nᵗʰ term of AP is given by,

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

⇒ t₁₆ = 3 + ( 16 - 1 ) * 5

⇒ t₁₆ = 3 + 15 * 5

⇒ t₁₆ = 3 + 75

⇒ t₁₆ = 78

∴ The 16ᵗʰ term of the AP is 78.

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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

Answer 2

$\implies \: a = 3 \\ \\ \implies \: d = 5 \\ \\ we \: know \: that \: ap \: nth \: term \: formula \\ \\ \implies \pink{ a_{n} = a + (n -1 )d} \\ \\ \implies \: a_{16} = 3 + (16 - 1)5 \\ \\ \implies \: 3 + 15 \times 5 \\ \\ \implies \: 3 + 75 \\ \\ \implies \boxed{\red{ a_{16} = 78}}$

16th term is=78

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