Question

Q.Find the number of multiples of 8 between 1 and 300?
Chapter 5->Arithmetic Progression.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Number\:of\:terms=37\:terms}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Series = 8,16,24,32,....,296 \\ \\ \tt: \implies First \: term = 8 \\ \\ \tt: \implies Last \: term = 296 \\ \\ \tt : \implies Common \: difference = 8 \\ \\ \red{\underline \bold{To \: Find:}}\\ \tt: \implies Number \: of \: terms = ?$

• According to given question :

$\tt \circ \: a = 8 \\ \\ \tt \circ \: d = 8 \\ \\ \tt \circ \: a_{n} =296 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1)d \\ \\ \tt: \implies 296 = 8 + (n - 1) \times 8 \\ \\ \tt: \implies 296 - 8 =( n - 1) \times 8 \\ \\ \tt: \implies \frac{288}{8} = n - 1 \\ \\ \tt: \implies 36= n - 1 \\ \\ \tt: \implies n = 36+ 1 \\ \\ \green{\tt: \implies n = 37 \: terms} \\ \\ \green{\tt \therefore Number \: of \: terms \: is \: 37 }$

Answer 2

Given:-

Multiples of 8 between 1 and 300 are:

8, 16, 24, ......., 296

The above multiples of 8 between 1 and 300 are in an AP.

So, we can say that,

• a = 8

• d = 16-8 = 8

• a$n$ = 296

To find:-

n (number of multiples)

Solution:-

We know,

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

⇒296 = 8 + (n-1)8

⇒296-8 = (n-1)8

⇒288 = (n-1)8

⇒288/8 = (n-1)

⇒36 = n-1

⇒n = 36 + 1

⇒$\boxed{\bold{n=37}}$

∴So, there are 37 multiples of 8 between 1 and 300.