Question

consider the number which are multiple of 7 in between 100and 400.find the sum of terms​

Answer 1

Answer:

we can applying 7 into 10 =70

and 70 into 2 = 140

so 7 divides 70 and 70 divedes 140

then 7 also devides 140

Answer 2

Answer:-

• Sequence of numbers that are multiples of 7 between 100 and 400 is 105 , 112 , 119... , 399.

If we assume that this sequence is in AP,

• a = 105
• d = 112 - 105 = 7
• nth term or a(n) = 399

We know that,

nth term of an AP = a + (n - 1)d

→ 399 = 105 + (n - 1)(7)

→ 399 - 105 = 7n - 7

→ 294 + 7 = 7n

→ 301 = 7n

→ 301/7 = n

→ 43 = n

We know,

Sum of first n terms of an AP = n/2 * [ a + a(n) ]

→ Sum of the numbers = 43/2 * [ 105 + 399 ]

→ Sum of the numbers = 43/2 [ 504 ]

→ Sum of the numbers = 43 * 252

→ Sum of the numbers = 10,836.

Therefore, there are 43 numbers which are multiples of 7 and their sum is 10,836.