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find the Sum of all Multiple of 9 lying Between 300 and 700




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Answer 1

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▶ 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.

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Answer 2

this is an arithmetic progression
the multiple lying between 300 and 700 are
306,315, ......693
first term a=306 and common diffrence =9
apply a=a+(n-1)d