In an arithmetic sequence the sum of the first n n terms is given by u1+⋯+un=Sn=n2−10n. u 1 + ⋯ + u n = S n = n 2 − 10 n . Find u103.

Answer 1

sum of an arithmetic sequence = u1+u2+....+un = (n/2)(u1 + un) which = n^2 -10n in the given problem

u1 +un = n(n-10)(2/n) 2n-10

u1 + u103 = 2(103)-10 = 206-10 = 196

u103 = 196-u1

if u1 =1

then

u103 = 102

and d= 1

if u1 =2

then u103 = 101

if u1 =51

u103 = 52

and d= 1/102

if u1 =102

u103 = 0

and d=-1