Question

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

Answer 1

a(First multiple)=306

last multiple=693

d=9

therefore,

693=306+(n-1)*9

693=306+9n-9

693=297+9n

9n=693-297

9n=396

n=396/9

n=44

no. of terms =44

Sum= 44/2(306+693)

sum=22*999

sum=21978.

Sum= 21978

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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