shrive555 wrote:

How many multiples of 5 are there between 81 and 358?

54

55

56

57

58

i tried this formula \(Sum = \frac{a1+an}{2}*n\)

How did you use this formula? We don't have the sum of all terms and we don't have n.

Focus on the logic here: Multiples of 5 between 81 and 358 are 85, 90, 95, 100.....350, 355

Question is: How many numbers are they?

85

90 = 85 + 1*5

95 = 85 + 2*5

100 = 85 + 3*5

.

.

.

355 = 85 + 54*5

Total 55 terms.

To get the 54 above, you would need to do the following: (355 - 85)/5

The point is, this is an arithmetic progression.

a, a + d, a + 2d, a + 3d ........ a + nd

Total number of terms = n + 1

The last term (355) is first term(85) plus n times the common difference(5).

355 = 85 + n*5

Solve this to get n as 54

Total number of terms = 54 + 1 = 55

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