Question

the sum of n term of an AP is 2n2+n then 8th term of the AP is

Answer 1

Given sum of n terms of an AP sn = 2n^2 + n.

Substitute n = 1.

= > sn = 2(1)^2 + 1

= > 3.

So, First term is a = 3.

Substitute n = 2:

= > s(2) = 2(2)^2 + 2

= > 10.

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Now,

= > 3 + a2 = 10

= > a2 = 7.

Common difference d = a2 - a1

= > 7 - 3

= > 4.

Here,

We need to find 8th term, So:

= > a + (8 - 1) * d

= > 3 + (7 - 1) * 4

= > 3 + (6) * 4

= > 27.

Therefore the 8th term of an AP is 27.

Hope this helps!

Answer 2

SUM OF AP

@n = last term

Sn = n/2 { a + @n}

2n^2 + n = n/2{a + @n}

2n + 1 = 1/2 { a + @n}

4n + 2 = a + a + (n-1)d

4n + 2 = 2a + nd - d

then compare

2a -d = 2 -----------------> EQ 1.

nd = 4n ------------------------> EQ 2.

then


d = 4. ( by EQ 2.)

a = 3



then 8th term of AP

@n = a+ (n-1)d


then 8th term

@8 = a + 7d

= 3 + 7(4)

= 3 + 28

= 31