Question

If the sum of the n terms of an AP is 1/2[3n^2 +7n] then find its nth term hence write its 20th term

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Here

S(n) = 1/2{3n² + 7n}

= 1/2{3 × (1)² + 7(1)}

= 1/2(3 + 7)

= 1/2 × 10

= 5

Now,

S(2) = 1/2{3(2)² + 7 × 2}

= 1/2(12 + 14)

= 1/2 × 26

= 13

As here,

a(1) = S(1) = 5

a(2) = S(2) - S(1)

= 13 - 5

= 8

Also,

a(2) = S(2) - a(1)

= 8 - 5

= 3

Here we get,

Arithmetic Progression = 5, 8 , 11 , 14 , 17 , ......

Now,

Using Formula we have,

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

= 5 + (n - 1) × 3

= 3n + 2

Also,

a(20) = 3 × 20 + 2

= 62

Therefore,

20th term = 62