Question

find the sum of series two cube minus one plus 4 cube minus 3 Cube + 6 cube - 5 cube to find the n term and 8th term​

Answer 1

Answer:

2³- 1 + 4³ - 3³ + 6³ - 5³ = (8-1) + (64 - 27) + (216 - 125)

8th term = 7³ = 343

nth term = nth term = (n*2)³ if n is at odd place

(n*2 - 1)³ if n is at even place

Answer 2

the 8th term would be -7³

Given portion of series is  2³-1³+4³-3³+6³-5³+.......

The given series consist of two sub-series :

1) 2³+4³+6³+.......

2) -1³-3³-5³+.......

The nth term of the series will depend on whether it is a part of first series or second series

Case 1 : If n is odd

nth term would be (n+1)³

Case 2 : If n is even

nth term would be -(n-1)³

Finding the 8th term, since n is even:

nth term would be -(n-1)³ i.e. 8th term would be -(8-1)³ = -7³ = -343