Question

the sum of n terms of an ap is given by SN equals to 3n square + 5n which of its term is 164​

Answer 1

Answer:

So 27thterm is 164.

Step-by-step explanation:

Sn=3n2+5n

S1=a1=3(1)2+5(1)=8

S2=3(2)2+5(2)=22

S2=22=a1+a2

a2=22-8=14

d=a2-a1=14-8=6

nth term value is 164,then what is n?

nth term=a+(n-1)d

164=8+(n-1)6

164-8 / 6=n-1

156/6=n-1

26+1=n

n=27

So 27thterm is 164.

Answer 2

27th term is 164

Given

Sum of n terms of an AP is given by Sₙ = 3n² + 5n

To Find

Which of it's term is 164

Knowledge Required

$\bf \pink{\bigstar\ \; S_n=\dfrac{n}{2}(2a+(n-1)d)}\\\\\bf \green{\bigstar\ \; a_n=a+(n-1)d}$

Solution

Given ,

$\rm S_n=3n^2+5n\\\\\to \rm S_1=3(1)^2+5(1)\\\\\to \rm S_1=3+5\\\\\to \rm S_1=8\\\\\to \bf a=8$

Now ,

$\rm S_2=3(2)^2+5(2)\\\\\to \rm S_2=3(4)+10\\\\\to \rm S_2=22\\\\\to \rm a_1+a_2=22\\\\\to \rm a+a+d=22\\\\\to \rm 2a+d=22\\\\\to \rm 2(8)+d=22\\\\\to \bf d=6$

Now , we need to find which term is 164 .

$\to \rm a_n=164\\\\\to \rm a+(n-1)d=164\\\\\to \rm 8+(n-1)6=164\\\\\to \rm 8+6n-6=164\\\\\to \rm 6n+2=164\\\\\to \rm 6n=162\\\\\to \bf \blue{ \; n=27\ \; \bigstar}$

So , 27th term is 164