Question

find the first two terms of the sequence Sn =n² (n+1)

Answer 1

S1 = a1 = 1²(1+1)= 1*2=2
a2 = S2 - S1 = 2²(2+1) - 1²(1+1)
= 4*3 - 1*2
= 12 - 2 = 10
so first two terms are 2, 10..

Answer 2

Answer:

First term $a_{1}=2$

Second term $a_{2}=10$

Step-by-step explanation:

$Given\:Sequence\:S_{n}\\=n^{2}\times (n+1)$ ---(1)

i ) Substitute n=1 in Equation (1), we get

$First\: term =a_{1}\\=S_{1}=1^{2}(1+1)$

=$1\times 2$

=$2$ ---(2)

ii) Substitute n=2 in equation (1), we get

$S_{2}=2^{2}(2+1)$

=$4\times 3$

=$12$ ---(3)

Now ,

iii) Second term in given sequence = $a_{2}=S_{2}-S_{1}$

=$12-2$ /* From (2)&(3)

=$10$

Therefore,

First term $a_{1}=2$

Second term $a_{2}=10$

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