Question

Identify a relationship among Tn ,Sn and Sn-1 where n;1 and n€N

Answer 1

Answer:

Tn =a+(n-1)d

Sn=n/2(2a+(n-1)d)

Answer 2

The relationship among them is $S_n- S_n_-_1 = T_n$

Step-by-step explanation:

relationship among Tn ,Sn and Sn-1

$S_n$ is the sum of n terms in an AP

$S_n_-_1$ is  the sum of n-1 terms in an AP

$T_n$ is the nth term in the AP

then

$S_n = \frac{n}{2}(2a+(n-1)d)..(1)\\\\S_(n-1)= \frac{n-1}{2}(2a+(n-2)d)..(2)$

T_n = a+(n-1)d

adding equation 1 and 2 we get

$S_n- S_n_-_1 = T_n$

hence , The relation ship among them is $S_n- S_n_-_1 = T_n$

#Learn more:

If x, y, z are 3 consicutive terms of an arthemetic sequence find 2 different relation ship among them

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