Question

2. How many integers divisible by 6 lie between - 30 and 39​

Answer 1

$\bold\blue{Question}$

How many integers divisible by 6 lie

between - 30 and 39 ?

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

There are 11 integers divisible by 6 lie between -30 and 39.

$\bold\purple{Explanation}$

There will be difference of 6 in between integers which are divisible by 6 and lie between -30 and 39.

This will form A.P.

$\bold\blue{Given:}$

Integers lies between -30 and 39

$\bold\pink{To \ find:}$

Number of integers which are divisible by 6.

$\bold\green{\underline{\underline{Solution}}}$

Integers which are divisible by 6 and lie between -30 and 39 are

-24,-18,-12,...,36

Here,

-18-(-24)=6

-12-(-12)=6

Therefore the common difference is 6 and sequence forms an A.P.

In this sequence,

t1=a=-24,d=6 and tn=36

tn=a+(n-1)d....formula

36=-24+(n-1)6

6(n-1)=36+24

6(n-1)=60

n-1=$\bold{\frac{60}{6}}$

n=10+1

n=11

$\bold\purple{There \ are \ 11 \ integers \ divisible \ by \ 6}$

$\bold\purple{which \ lie \ between \ -30 \ and \ 39.}$

Answer 2

Answer:

how many integers divisible by 6 lie between 30 and 39