Question

Find the sum of all integers between 10 and 200 which are divisible by 7

Answer 1

Answer:

this is an arithmetic progression.thus there are 27 numbers in between 10 and 200 that are exactly divisible by 7

14, 21, 28,32,49,56,63,70,77,84,91,98,105,11,2,119,126,133,140,147,154,161,168,175,182,189,195=27 number between 10 and 200 divisible by 7

Answer 2

Step-by-step explanation:

Integers divisible by 7 between 10 and 200 are given as:

14, 21, 28, 35,............196

Here

$a = 14 \\ d = 7 \\ a_n \: = 196 \\ \because \: a_n = a + (n - 1)d \\ \therefore \: 196 = 14 + (n - 1) \times 7 \\ 196 - 14 = 7(n - 1) \\ 182 = 7(n - 1) \\ n - 1 = \frac{182}{7} \\ n - 1 = 26 \\ n \: = 26 + 1 \\ n = 27 \\ thus \: there \: are \: total \: 27 \: terms \: \\ between \: 10 \: and \: 200 \: which \: are \: \\ completely \: divisible \: by \: 7. \\ now \: by \: sum\: of \: n \: terms \: of \: an \: ap \\ S_n = \frac{n}{2} (a + a_n) \\ S_{27} = \frac{27}{2} (14 + 196) \\ = \frac{27}{2} \times 210 \\ = 27 \times 105 \\ = 2835$