Find the 6 t h term of 1 + x 2 - 5 .

Given, 1 + x 2 - 5 T r + 1 in 1 + x - n = - 1 r ( n ) ( n + 1 ) ( n + 2 ) … ( n + r - 1 ) r ! · x r Put r = 5 , n = 5 and x = x 2 ⇒ T 6 = - 1 5 ( 5 ) ( 5 + 1 ) ( 5 + 2 ) ( 5 + 3 ) ( 5 + 4 ) 5 ! · x 2 5 = - 5 · 6 · 7 · 8 · 9 1 · 2 · 3 · 4 · 5 · 1 2 5 · x 5 = - 63 16 · x 5 ∴ 6 t h term in 1 + x 2 - 5 is - 63 16 · x 5 .

Find the 7 t h term of 1 - x 2 3 - 4 .

Given, 1 - x 2 3 - 4 T r + 1 in 1 - x - n = ( n ) ( n + 1 ) ( n + 2 ) … ( n + r - 1 ) r ! · x r Put r = 6 , n = 4 and x = x 2 3 ⇒ T 7 = ( 4 ) ( 4 + 1 ) ( 4 + 2 ) ( 4 + 3 ) ( 4 + 4 ) ( 4 + 5 ) 6 ! - x 2 3 6 = 4 · 5 · 6 · 7 · 8 · 9 1 · 2 · 3 · 4 · 5 · 6 · x 12 3 6 = 28 243 · x 12 ∴ 7 t h term in 1 - x 2 3 - 4 is 28 243 · x 12 .

Find the 10 t h term of ( 3 - 4 x ) - 2 3 .

Given, ( 3 - 4 x ) - 2 3 = 3 1 - 4 3 x - 2 3 = 3 - 2 3 1 - 4 3 x - 2 3 Now, 10 t h term in 1 - 4 3 x - 2 3 The general term of ( 1 - x ) - p q is T r + 1 = ( p ) ( p + q ) ( p + 2 q ) … [ p + ( r - 1 ) q ] ( r ) ! x q r Here, p = 2 , q = 3 , r = 9 Then, T 10 = ( 2 ) ( 2 + 3 ) ( 2 + 6 ) … [ 2 + ( 9 - 1 ) 3 ] 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 4 9 x 9 = 2 · 5 · 8 … ( 26 ) 9 ! 4 x 9 9 ∴ 10 t h term in ( 3 - 4 x ) - 2 3 is 3 - 2 3 2 · 5 · 8 … ( 26 ) 9 ! 4 x 9 9

Find the 5 t h term of 7 + 8 y 3 7 4 .

Given, 7 + 8 y 3 7 4 = 7 1 + 8 y 21 7 4 The general term of ( 1 + x ) p q is T r + 1 = ( p ) ( p - q ) ( p - 2 q ) … [ p - ( r - 1 ) q ] ( r ) ! x q r Here, p = 7 , q = 4 , r = 4 ∴ T 5 of 1 + 8 y 21 7 4 = ( 7 ) ( 7 - 4 ) ( 7 - 2 × 4 ) ( 7 - 3 × 4 ) 1 × 2 × 3 × 4 2 y 21 4 = 7 ( 3 ) ( - 1 ) ( - 5 ) 1 × 2 × 3 × 4 · 2 4 y 4 ( 21 ) 4 = 70 y 21 4 ∴ 5 t h term in 7 + 8 y 3 7 4 is 7 7 4 70 y 21 4