Question

2.2और 100 के बीच की सभी विषम संख्याओं का योगफल ज्ञात कीजिए जो 3 से विभाजित हो
3.8के प्रथम 15 गुणों का योग ज्ञात कीजिए।​

Answer 1

Answer:

2. Given,

The odd numbers which are multiple of 3 between 2 and 100,

3, 6, 9, 12, ...............................99

Which is an AP,

Having First term, a = 3,

Common difference, d = 3,

Last term = 99

Let n be the number of terms,

$3+(n-1)3 = 99\implies 3 + 3n - 3 = 99\implies 3n = 99\implies n = 33$

Hence, the sum of the all odd numbers which are multiple of 3 between 2 and 100,

$S_{33}=\frac{33}{2}(2(3)+(33-1)3)$

$=\frac{33}{2}(6+96)$

$=\frac{33}{2}(102)$

$=1683$

3. Given,

The first 15 multiple of 8,

8, 16, 24, 32,.......

Which is an AP,

Having First term, a = 8,

Common difference, d = 8,

Number of terms = 15

Hence, the sum of the first 15 multiple of 8,

$S_{15}=\frac{15}{2}(2(8)+(15-1)8)$

$=\frac{15}{2}(16+112)$

$=\frac{33}{2}(128)$

$=2112$