Question

in an A.P the first term is 8 , nth term is 33 and the sum to first n terms is 66 .find n and d , the common difference

Answer 1

hi Anshika!
#ur Ans
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Here given that
first term => a = 8

9th term => l = 33

sum of first n terms Sn = 66

We know that

Sn = [ n(a+l) ] /2

66 = [ n(8+33)]/2

66 = [ 41n]/2

41n = 132

n = 132/41 or 3.21

l= a + (n - 1)d

33 = 8 +( 3.21-1) d

33 = 8+2.21d

2.21d = 33-8

d = 25/2.21

d = 2500/221 or 11.31 Ans

Answer 2

Answer:

first term=a=8

 nth term=l=33

 sum to first n terms=Sn=123

Sn=[n(a+l)]2

123=n(41)/2

n=6

l=a+[n-1]d

33=8+5d

d=5