Find the sum of all integers between 50 and 450 which are divisible by 7
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Answers
Answer:
The sum of all integers between 50 and 450 divisible by 7 is 14,364
Step-by-step Explanations :
To find : Sum of all the integers between 50 and 450 which are
divisible by 7.
We know that,
After 50,56 is the first number which is divisible by 7 and
Before 450, 448 is the last number which is divisible by 7.
AP = 56,63,....448
∴ a = 56 , d = 7 , Tn = 448
We know that,
Tn = a + (n-1)d
448 = 56 + (n-1) × 7
448 = 56+ ( n - 1) × 7
448 = 56 + 7n - 7
448 - 56 + 7 = 7n
392 + 7 = 7n
399 = 7n
n = 399/7
n = 57
We know that ,
Sn = n/2 × ( 2a + ( n - 1 ) × d.
= 57/2 × ( 2 × 56 + ( 57 - 1 ) × 7
= 28.5 × ( 112 + 392 )
= 28.5 × 504
= 14,364
Hence, the sum of all integers between 50 and 450 divigible by 7 is 14,364