The sum of first n terms of an A.P. is 5n — 2n². Find the A.P. i.e. a and d.

Formula used.

S_n = [2a + (n–1)d]

S_n = [2a + (n–1)d]

5n – 2n² = [2a + (n–1)d]

2×n[5 – 2n] = n[2a + (n–1)d]

10 – 4n = (2a–d) + nd

Then

Real part should be equal to Real

And imaginary part should be equal to imaginary

2a – d = 10 ......eq 1

nd = –4n

⇒ d = –4

Putting value of d in eq 1

2a – d = 10

2a – (–4) = 10

2a + 4 = 10

2a = 10 – 4 = 6

⇒ a = = 3