Question

23rd term of an arithmetic sequence is 32. 35th term is 104.
a) What is its common difference?
b) What is its 17th term?
c) Find the sum of the first 33 term 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

Answer 2

Answer:

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