Question

Find the sum of all multiples of 9 lying between 300 and 900

Answer 1

here A.P. formed is 306, 315, 324, .......... , 693

here ,the first term a=306 and the common difference d=9Last term
(l)=693

Let there be n terms in this A.P.

Then,nth term=la+(n-1)d=693306+(n-1)9=693(n-1)9=693-306(n-1)9=387n-1=387/9n-1=43n=43+1n=44

Hence,44 multiples 0f 9 lie between 300 and 700.

Sum = n/2(a + l)= 22(306 + 693)= 21978

Answer 2

HEY THERE!!!


Question;-

Find the sum of all multiples of 9 lying between 300 and 700.


Method of Solution;-

Firstly, find which number lies on sum of all multiples of 9 lying between 300 and 700.

Number which are multiples of 9 lying between 300 and 700 Given Below in the form of Arithmetic Sequence or Progression.


306, 315, 324, 333, ..., 693.

here,
 a = 306, d = (315 - 306) = 9 and l = 693.

Let the number of terms be n.
Then Tn = 693


⇒ a + (n - 1)d = 693


= 306 + (n - 1​) 9 = 693


= 9n = 396

= n = 44

∴ Required sum = n /2(a+l)
                  ‎‎‎‎‎‎‎‎‎= 44/2(306+693)
‎ =22(306+693)
‎
‎ =22(999)
‎
‎ =21978

Hence, sum of all multiples of 9 lying between 300 and 700 = 21,978