the sum of n terms of an Ap is 3n2+5n find the Ap hence find its 16th term
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Answered by
376
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
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
Answered by
183
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
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