Question

If tn = n, find Sn and evaluate S100.

Answer 1

given, $T_n=n$

we can write it , $T_n=1+(n-1)1$
now if we compare it with $T_n=a+(n-1)d$
we get, a = 1 and d = 1

so, $S_n=\frac{n}{2}(a+T_n)$
= n/2(1 + n)
= n(n +1)/2

$S_{100}$ = 100(100+1)/2 = 5050

Answer 2

Answer:

Sn = n/2 (a1 + an) , S100 =  5050

Step-by-step explanation:

Tn = n

T1 = 1  

T100 = 100

Find Sn:

Sn = n/2 (a1 + an)

Sn = n/2(1 + an)

Find S100:

Sn = n/2 (a1 + an)

S100 = 100/2 (1 + 100) = 5050

Answer: Sn = n/2 (a1 + an) , S100 =  5050