Question

how many numbers are there in between 50 and 150 which are exactly divisibly by 7

Answer 1

Hey !!

Numbers which are divisible by 7 between 50 and 150 are ;

56 , 63 , 70........147.

AP = 56 , 63 , 70......147

Here,

First term ( A ) = 56

Common difference ( D ) = 63 - 56 = 7

Last term ( Tn ) = 147

Number of terms = ?

Tn = 147

A + ( n - 1 ) × D = 147

56 + ( n - 1 ) × 7 = 147

56 + 7n - 7 = 147

7n + 49 = 147

7n = 147-49

n = 98/7 = 14 .

Hence,

14 numbers are divisible by 7 between 50 and 150.

Answer 2

Concept

The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Its other name is Arithmetic Sequence.

Given

It is given that there are numbers between 50 and 150 which are divisible by 7

Find

We need to find the numbers between 50 and 150 which are divisible by 7

Solution

Numbers which are divisible by 7 between 50 and 150 are ;

56 , 63 , 70........147.

AP = 56 , 63 , 70......147

Here,

First term ( A ) = 56

Common difference ( D ) = 63 - 56 = 7

Last term ( Tn ) = 147

We need to find the number of terms  that is n

So , Taking the last number of the series

Tn = 147

A + ( n - 1 ) × D = 147

56 + ( n - 1 ) × 7 = 147

56 + 7n - 7 = 147

7n + 49 = 147

7n = 147-49

n = 98/7 = 14 .

Hence,14 numbers are divisible by 7 between 50 and 150.

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