Question

How many terms of an A.P. 17,25,…. must be taken to give the sum of 636?

Answer 1

Answer:

11

Step-by-step explanation:

Sn=n/2(2a+(n-1)d)

636=n/2(2×17+(n-1)8)

636=n/2(34+(n-1)8)

636=n/2(34+8n-8)

636=n/2(26+8n)

636×2=n(26+8n)

1272=26n+8n^2

1272=2(13n+4n^2)

1272/2=13n+4n^2

636=13n+4n^2

4n^2+13n-636=0

According to shridharacharya formula:-

n=-b+-√b^2-4ac/2a

n=-13+-√169-16×636/8

n=-13+-√10007/8

n=-13+-100.03/8

n=-13-100.03/8

=-113.03/8

=-14.12(neglected)

OR

n=-13+100.03/8

n=87.03/8

n=10.87

n=11(approx)

Hope you understand:):)

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Answer 2

Step-by-step explanation:

a=17

d= 8

Sn= 636

Sn = n{2a+(n-1)d}/2

636= n{ 2×17 +(n-1) 8}/2

636×2= n ( 34 + 8n-8)

1272= n( 26 + 8n)

1272= 8n^2 +8n

8n^2+8n -1272 =0

n^2 + n - 159 =0