Question

find the sum of all multiples of 7 lie between 500 & 900

Answer 1

Answer:-

39900.


Step by step explanation

Hope it helps!

Answer 2

Hii Mate !!


Here is your answer :


Question : Find the sum of all multiples of 7 lie between 500 and 900.


Solution :



Let a be the first term and d be the common difference of the an AP .



Numbers which are lie between 500 and 900 also which are divisible by 7 are : 504 , 511 , 518 , .......... , 896.


Here,

First term. ( a ) = 504


Common difference ( d ) = 511 - 504 = 7 .


And ,


Last term ( Tn ) = 896


a + ( n - 1 ) * d = 896


504 + ( n - 1 ) * 7 = 896


504 + 7n - 7 = 896


7n + 497 = 896


7n = 896 - 497

7n = 399

n = 399/7


n = 57.


Therefore,

Number of terms = 57.


Sn = n /2 × [ 2a + ( n - 1 ) * d ]


S15 = 57/2 × [ 2* 504 + ( 57 - 1 ) * 7 ]


=> 57/2 × ( 1008 + 56 * 7 )


=> 57 / 2 × 1008 + 392


=> 57/2 × 1400


=> 57 × 700


=> 39900.


Hence,

The sum of all multiples of 7 between 500 and 900 is 39900.


Hope it helps you ♥


By Rishi403.

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