Question

find the number of terms an a.p 3,6,9,12.....111​

Answer 1

Answer:

The number of terms an AP 3,6,9,12----------- 111​ is 37.

Step-by-step explanation:

The given sequence is an AP

The first term (a) =3

and common difference (d) = second number - first number = 6 -3 = 3.

Let there be n terms in the given sequence.

Then, nth term=111

Formula: $a_n= a + (n - 1) d$

a + (n − 1)d = 111

3 + (n − 1) × 3 = 111

3 + 3n - 3 = 111

3n = 111

n = 111/3

n = 37

Thus, the given sequence contains 37 terms.

Answer 2

Final answer:

The number of terms in the given AP sequence is 37 terms

Given:

The AP sequence 3 , 6 , 9 , 12 . . . . . 111

To find:

The number of terms in the given AP sequence.

Formula to be used:

$a_n = a+ (n-1)d$

Solution:

The AP sequence 3 , 6 , 9 , 12 . . . . . 111

We can find the number of terms in the given AP sequence by using the following formula,

$a_n = a+ (n-1)d$

First term, a = 3

Common difference, d = 6 - 3

d = 3

$a_n$ = 111

111 = 3 + ( n - 1 ) × 3

111 = 3 + 3n - 3

111 = 3n

n = $\frac{111}{3}$

n = 37

Thus, the given sequence contains 37 terms.