Write first 4 terms of the sequence a n = ( − 1 ) n − 1 × 2 n + 1

Given: a n = ( − 1 ) n − 1 × 2 n + 1 The first 4 terms can be obtained by putting n = 1 , 2 , 3 , 4 . a 1 = ( − 1 ) 1 − 1 × 2 1 + 1 = 1 0 × 2 2 = 4 a 2 = ( − 1 ) 2 − 1 × 2 2 + 1 = - 1 × 2 3 = - 8 a 3 = ( − 1 ) 3 − 1 × 2 3 + 1 = - 1 2 × 2 4 = 16 a 4 = ( − 1 ) 4 − 1 × 2 4 + 1 = - 1 3 × 2 5 = - 32 ∴ First four terms are 4 , - 8 , 16 , - 32 .

Write first 4 terms of the sequence a n = ( − 1 ) n − 1 × 2 n + 1

Given: a n = ( − 1 ) n − 1 × 2 n + 1 The first 4 terms can be obtained by putting n = 1 , 2 , 3 , 4 . a 1 = ( − 1 ) 1 − 1 × 2 1 + 1 = 1 0 × 2 2 = 4 a 2 = ( − 1 ) 2 − 1 × 2 2 + 1 = - 1 × 2 3 = - 8 a 3 = ( − 1 ) 3 − 1 × 2 3 + 1 = - 1 2 × 2 4 = 16 a 4 = ( − 1 ) 4 − 1 × 2 4 + 1 = - 1 3 × 2 5 = - 32 ∴ First four terms are 4 , - 8 , 16 , - 32 .

Find first 5 terms of the sequence, defined by a 1 = − 1 , a n = a n − 1 n for n ≥ 2 .

Given: a 1 = − 1 , a n = a n − 1 n for n ≥ 2 . Since a 1 is given. So, the remaining 4 terms can be obtained by putting n = 2 , 3 , 4 , 5 . Therefore, a 2 = a 2 − 1 2 = a 1 2 = - 1 2 a 3 = a 3 - 1 3 = a 2 3 = - 1 2 3 = - 1 6 a 4 = a 4 - 1 4 = a 3 4 = - 1 6 4 = - 1 24 a 5 = a 5 - 1 5 = a 4 5 = - 1 24 5 = - 1 120 So, first five terms are − 1 , − 1 2 , − 1 6 , − 1 24 , − 1 120 .