Question

in an ap if Sn = 3n(squared) + 5n and Ak = 164 find k

pls pls solve it is very urgent

Answer 1

hello I hope you understand dear
,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.

dude :-)

Answer 2

ak = an = 164

Sn = 3n2 + 5n

S1 = 3 x ( 1 ) 2 + 5 x 1 = 3 + 5 = 8

S2 = 3 x ( 2) 2 + 5 x 2 = 12+ 10 = 22

a1 = S1 = 8

a2 = S2- S1 = 22 - 8 = 14

d = a2 - a1 = 14 - 8 = 6

a= 8

d= 6

an = 164

an = a +( n-1 ) d

164 = 8 + ( n-1 ) 6

164 = 8 + 6n - 6

164 = 2 + 6n

164 -2 = 6n

162 = 6n

162/ 6 = n

27 = n

i.e. n = 27

Therefore k is 27