Find the indicated terms in each of the sequences whose n^th terms are given by

(i) (ii) a_n = (-1)ⁿ 2^{n + 3} (n + 1); a₅, a₈

(iii) a_n = 2n² – 3n + 1; a₅, a₇ (iv) a_n = (-1)ⁿ (1 – n + n²); a₅, a₈

(i) Here, a_n =

For n = 7, a₇ = = =

For n = 9, a₉ = = =

(ii) Here, a_n = (-1)ⁿ 2^{n + 3} (n + 1)

For n = 5, a₅ = (-1)⁵ 2^{5 + 3} (5 + 1) = (-1) 2⁸ (6) = -6 (256) = -1536

For n = 8, a₈ = (-1)⁸ 2^{8 + 3} (8 + 1) = (1) 2¹¹ (9) = 9 (2048)

= 18432

(iii) Here, a_n = 2n² – 3n + 1

For n = 5, a₅ = 2(5)² – 3(5) + 1 = 2(25) – 15 + 1 = 50 – 15 + 1

= 36

For n = 7, a₇ = 2(7)² – 3(7) + 1 = 2(49) – 15 + 1 = 98 – 21 + 1

= 78

(iv) Here, a_n = (-1)ⁿ (1 – n + n²)

For n = 5, a₅ = (-1)⁵ (1 – 5 + 5²) = (-1) (1 – 5 + 25) = (-1) (21)

= -21

For n = 8, a₅ = (-1)⁸ (1 – 8 + 8²) = (1) (1 – 8 + 64) = (1) (57)

= 57