find the sum of all integers between 100and400 which are divisible by 7
Answers
Answer:
The sum of all integer between 100 and 400 that are divisible by 7 is 2276
Step-by-step explanation:
First number after 100 which is divisible by 7 is 105. Next number is 112 and so on. The last number before 400 is 399.
So, the numbers between 100 and 400 divisible by 7 are 105,112,119…….399.
This is an AP with first term a = 105, common difference d = 7 and last term = 399.
Using the nth term formula an = a + (n-1)d,
399 = 105 + (n-1)7
399–105 = (n-1)7
294 = (n-1)7
n-1 = 42
So n= 43.
And the sum of AP is given by
Sn=n/2(a=1)
S43=243(105+1)S43=43(53)S43=2279
Answer:
Sn = 441
Step-by-step explanation:
105,112,119, ______, 336
a= 105
tn = 336
d = 7
tn = a+ ( n-1) d
336 = 105 +(n-1)7
336= 105 + 7n -7
336 = 98 +7n
336-98 = 7n
238 = 7n
238/7 = n
n= 34
Sn = 2a +(n-1)d
= 2(105) +(34-1)7
= 210 + (33)7
= 210 +231
Sn = 441