Question

13. Find the sum of the first 15 multiples of 8.
14. Find the sum of the odd numbers between 0 and 50.​

Answer 1

ANSWER:

ANSWER:Step-by-step explanation:

13.The first 15 multiples of 8 are 8,16,24,32,.... 15 times

First term = a = 8

Common difference = d = 16 - 8 = 8

n = 15

Applying formula, Sn=n2(2a+(n−1)d) to find sum of n terms of AP , we get

S15=152(16+(15−1)8)=152(16+112)=152(128)=15×64=960.

14.The odd numbers between 0 and 50 are 1,3,5,7,...49

It is an arithmetic progression because the difference between consecutive terms is constant.

First term = a = 1

Common difference = 3 - 1 = 2

Last term = l=49

We do not know how many odd numbers are present between 0 and 50. Therefore, we need to find n first.

Using formula an=a+(n−1)d, to find nth term of arithmetic progression, we can say that

49=1+(n−1)2

⇒49=1+2n−2

⇒50=2n

⇒n=502=25

Applying formula, Sn=n2(a+l) to find sum of n terms of AP , we get

S25=252(1+49)=252(50)=25×25=625.

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Answer 2

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