Question

If the sum of n terms of an ap is 3n^2+5n find the ap and hence find te 16th term

Answer 1

HEYA FRIEND!!
THIS IS YOUR REQUIRED ANSWER.

→Sn = 3n²+5n

→S1 = 3(1)²+5(1)
= 3+5
= 8
similarly,
→S2 = 3(2)²+5(2)
= 3*4+10
= 12+10
= 22
and
→ S2 = a1+a2
22 = 8+a2
a2 = 22-8
a2 = 14

→d = a2-a1
= 14-8
= 6

→a16 = a+15d
= 8+15*6
= 8+90
= 98

HOPE IT HELPS!!

REGARDS
★KHUSHI★

Answer 2

hey there ,

we know that

=) tn = s(n+1) -sn

=) tn = 3(n+1)^2 +5(n+1) -(3n^2 +5n)

=) tn = 3(n^2 +2n +1 ) +5n +5 - 3n^2 - 5n

=) tn = 3n^2 +6n +3 +5n +5 - 3n^2 -5n

=) tn = 6n +8

now ,

=) t1 = 14

==) t2 = 20

====) t3 = 26

now , ap is ... 14 , 20 , 26 , 32 .....so on

◆16th term = t16 = 16×6 +8 =104 ans ...

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hope it will help u