Question

How many multiples of 3 lie between 14 and 310.

Answer 1

Answer:

99

Step-by-step explanation:

AP formed: 15, 18, ..... ,309

309=15+(n-1)3

294=(n-1)3

98=n-1

n=99

Answer 2

The total number of terms which is multiples of 3 lie between 14 and 310 = 99

Step-by-step explanation:

The multiples of 3 lie between 14 and 310 are:

15, 18, ................ ,309

The given sequence are in AP.

Here, first term (a) = 15, common difference (d) = 18 - 15 = 3 and

$a_{n}$ = 309

Let n be the number of terms.

To find, the total number of terms which is multiples of 3 lie between 14 and 310 = ?

We know that,

The nth term of an AP

$a_{n}$ = a + (n - 1)d

⇒  15 + (n - 1)3 = 309

⇒ (n - 1)3 = 309 - 15 = 294

⇒ n - 1 = $\dfrac{294}{3}$ = 98

⇒ n = 98 + 1 = 99

Thus, the total number of terms which is multiples of 3 lie between 14 and 310 = 99