Question

the sum of n terms of an Ap is 3n2+5n find the Ap hence find its 16th term

Answer 1

The sum of n terms of an A.P. = 3n2+5n

then sum of n-1 terms= 3(n-1)2+5(n-1)

So nth term of A.P will be Tn=3n2+5n- 3(n-1)2-5(n-1)= 3n2+5n-3n2-3+6n-5n+5=6n+2

in this way by putinng values of n= 1,2,3,4,5,6,7,_______n-1, n

we will get the AP as 8,14,20,26,32,38,44,____and the 16th term will be= 6*16+2=98

Answer 2

Sn = 3n^2 + 5n

Sn – 1 = 3(n – 1)^2 + 5(n – 1)

= 3(n^2 + 1 – 2n) + 5n – 5

= 3n^2 + 3 – 6n + 5n – 5

= 3n^2 – n – 2

an = Sn – Sn – 1 = 3n^2 + 5n – (3n^2 – n – 2)

= 6n + 2

AP is 8, 14, 20, ....................

a(16) => a + 15d = 8 + 15(6) = 98