Question

)23rd term of an as is 32.35th term is 104, then
a)what is the common difference?
b)which is the middle term of first 35 terms of this sequence?
c)find the sum of first 35 terms of this sequence?

Answer 1

Answer:

a) Common difference = 6

b) 17th term = -4

c) Sum of first 33 terms = -132

Step-by-step explanation:

Let the first term of an AP be a and the common difference be d

23rd term = a+22d=32

a = 32-22d - eqn (1)

35th term = a+34d=104

From eqn (1)

32-22d+34d=104

12d=104-32

12d=72

d=6

Thus, a =32-22(6) = 32-132 = -100

17th term = a+16d = -100+16(6)= -100+96 = -4

Sum of first n terms = n/2[2a+(n-1)d]

Sum of 1st 33 terms = 33/2[2(-100)+32(6)] = 33/2[-200+192]=33/2(-8)=-132

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