Question

how many terms are there is the sequence 3,6,9,12....111​

Answer 1

Answer:

in the AP a=3 and d=3

111 is last term

a +(n-1)d = 111

3+(n-1)3 =111

3+3n-3=111

3n=111

n=111/3

n=37

Answer 2

Answer:

There are 37 terms in the given sequence.

Step-by-step-explanation:

The given sequence is

3, 6, 9, 12,... 111.

• t₁ = 3
• t₂ = 6
• t₃ = 9

t₂ - t₁ = 6 - 3 = 3

t₃ - t₂ = 9 - 6 = 3

∴ t₂ - t₁ = t₃ - t₂

In this sequence, the difference between two consecutive terms is constant.

∴ The sequence is an Arithmetic Progression ( AP ).

Here,

• a = t₁ = 3
• d = t₂ - t₁ = 3
• tₙ = 111

We know that,

tₙ = a + ( n - 1 ) * d

⇒ 111 = 3 + ( n - 1 ) * 3

⇒ 111 - 3 = 3 ( n - 1 )

⇒ 108 = 3n - 3

⇒ 3n = 108 + 3

⇒ 3n = 111

⇒ n = 111 / 3

⇒ n = 37

∴ There are 37 terms in the given sequence.