Question

an = 3n+2

find the value of Sn-1​

Answer 1

(It must be Sn+1...... check it.... if not then answer is 3n² + 7n -2/2)

Put , n = 1

an = 3n+2

a1 = 3+2 => a1 = 5

Put, n=2

a2 = 6+2

a2 = 8

So a = 5

d = a2-a1 => 8-5= 3

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

Sn = n/2 ( 10 +(n-1)3)

Sn = n/2 ( 10 + 3n -3)

Sn = n/2 ( 7 + 3n)

Sn+1 = [n/2(7 + 3n)] +1

==> 7n + 3n²/2 + 1

==> 3n² + 7n +2/2

==> 3n² + (6+1)n +2/2

==> 3n² + 6n + n+2/2

==> 3n( n+2) +1(n+2)/2

==> (3n+1)(n+2)/2

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