Question

The sum of n terms of an A.P is given by Sn= 3n^2+5n , which of its term is 164?

Answer 1

Answer:

164 is the 27 th term of the given AP

Step-by-step explanation:

Given:-

The sum of n terms of an A.P is given by Sn= 3n^2+5n

To find:-

which of its term is 164?

Solution:-

The sum of n terms of an AP =Sn=3n²+5n

Put n=1,then

S1=3(1)²+5(1)

=>S1=3+5

=>S1=8

So,First term (a)=8

Put n=2 then

=>S2=3(2)²+5(2)

=>S2=3(4)+10

=>S2=12+10

= S2=22

Sum of first two terms=22

=>S2=a1+a2

=>22=8+a2

=>a2=22-8

=>a2=14

Second term(a2)=14

Now ,Common difference (d)=a2-a1=14-8=6

Common difference(d)=6

Given term =164

Let it be nth term of the given AP

an=164

we know that an=a+(n-1)d

=>8+(n-1)6=164

= 8+6n-6=164

=>6n+2=164

=>6n=164-2

=>6n=162

=>n=162/6

=>n=27

Answer:-

164 is the 27th term of the given AP

Check:

27 th term of the AP=a27

=a+26d

=>8+26(6)

=>8+156

=>164

a27=164

Used formula:-

If a is the first term ,d is the common difference and n is the no. of terms then the general term of the AP=an=a+(n-1)d

Answer 2

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