Question

find the sum of numbers between 200 and 300 that are divisible by 7 use arthmetic progression​

Answer 1

$\large \red { \sf \: AP=203,210,217....294}$

$\large \blue { \sf \:Sn=?}$

$\large \blue { \sf \:a = 203}$

$\large \blue { \sf \:d = 210 - 203 = 7}$

$\large \blue { \sf \:last \: term \: (l) = 294}$

$\large \red { \sf \:l = a + (n - 1) \times d}$

$\large { \sf \:=>294 = 230 + (n - 1) \times 7}$

$\large { \sf \:294=203+7n-7}$

$\large { \sf \:294+7=203+7n}$

$\large{ \sf \:301=203+7n}$

$\large { \sf \:301-203=7n}$

$\large { \sf \:98=7n}$

$\large { \sf \:7n = \frac{98}{7} }$

$\large \red { \sf \:n = 14}$

$\large \green{ \sf \:Sn= \frac{n}{2} [2a+(n-1)×d]}$

$\large{ \sf \: \frac{14}{2} [2×203+(14-1)×17]}$

$\large { \sf \:7×[406+13×7]}$

$\large \red { \sf \:7 \times 497 = 3479}$

$\large \green{ \sf \: \: the \: required \: answer \: is \: 3479}$

Answer 2

Answer :-

AP => 203,210,217...294.

Sn = ?

α=> 203

d=> 210-203

d=> 7

⠀⠀⠀l = α+(n-1)×d

=> 294 = 230+(n-1)×7

=> 294+7= 203+7n

=> 301=203+7n

=> 301-203=7n

=> 98= 7n

=> n= 98/7

⠀⠀⠀n = 14.

=> Sn= n/2 [(2α+n-1)×α]

=> 14/2[2×203+(14-1)×17]

=> 7×[406+13×7]

=> 7×497

=> 3479Ans.

The required answer.