Question

If the sum of n terms of an A.P is 3n²+5n and its m th term is 164, find the value of m.

Answer 1

S = 3n2 + 5n

S1 = a1 = 3 + 5 = 8

S2 = a1 + a2 = 12 + 10 = 22          

 ⇒ a2 = S2 - S1 = 22 - 8 =  14

S3 = a1 + a2 + a3  = 27 + 15 = 42

⇒a3 = S3 - S2 =  42 - 22 = 20

∴ Given AP is 8,14,20,.....

Thus a = 8 , d = 6         

Given tm = 164.

164 =  [a + (n -1)d]

164 =  [(8) + (m -1)6]

164 = [8 + 6m - 6]

164 = [2 + 6m]

162= 6m

m = 162 / 6.

∴ m = 27.

Answer 2

Answer:

m = 27

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.

.•. , m=27