Question

In an ap if sn=3n2+5n and ak=164 find the value of k

Answer 1

$\huge{\mathfrak{\underline{\underline{\red{Answer :-}}}}}$

K = 27

$\huge{\mathfrak{\blue{Explanation}}}$

Given:-

Sn = 3n² + 5......(1)

Solution :-

Put the value of n as 1in equation1

⇒S₁ = 3(1)² + 5(1)

⇒S₁= 3 + 5

⇒T₁ = 8

Now, put value of n as 2

⇒S₂ = 3(2)² + 5(2)

⇒S₂ = 12 + 10

⇒S₂ = 22

So, T₁ + T₂ = 22

⇒8 + T₂ = 22

⇒T₂ = 22 - 8

⇒T₂ = 14

$\rule{200}{2}$

Now,

First term(a) = 8

Common difference (d) = 14 - 8 = 6

ak(an) = 164

Using Formula

$\huge{\boxed{\boxed{\blue{a_{n} = a + (n - 1)d}}}}$

______________[Put Values]

⇒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

$\huge{\boxed{\boxed{\red{K = 27}}}}$

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.