Question

In an AP, if Sn = 3n2 + 5n and ak = 164, find the value of k.

Answer 1

Solution:-
Given: Sn = 3n² + 5n
S₁ = 3(1)² + 5(1) 
= 3 + 5 
T₁ = 8
S₂ = 3(2)² + 5(2)
= 12 + 10
= 22
So, T₁ + T₂ = 22
8 + T₂ = 22
T₂ = 22 - 8
T₂ = 14
Now,
a = 8 and d = 14 - 8 = 6
As ak = 164
or a + (k-1)d = 164
8 + (k-1)6 = 164
6k - 6 = 164 - 8
6k = 164 + 6 - 8
6k = 162
k = 162/6
k = 27
Answer.

Answer 2

Solution:-

Given: Sn = 3n² + 5n

S₁ = 3(1)² + 5(1) 

= 3 + 5 

T₁ = 8

S₂ = 3(2)² + 5(2)

= 12 + 10

= 22

So, T₁ + T₂ = 22

8 + T₂ = 22

T₂ = 22 - 8

T₂ = 14

Now,

a = 8 and d = 14 - 8 = 6

As ak = 164

or a + (k-1)d = 164

8 + (k-1)6 = 164

6k - 6 = 164 - 8

6k = 164 + 6 - 8

6k = 162

k = 162/6

k = 27

Answer.