Question

If an ap if sum of its first n terms is 3n+5n and its kth term is 164,find the value of k

Answer 1

Answer:

Step-by-step explanation:

Sn = 3n+ 5n

Let n= 1

S1= 3(1) + 5(1)

S1 = 3+5

S1 = 8

Let n = 2

S2= (3×2) +( 5×2)

S2 = 6+10

S2 = 16

Let n= 3

S3 = (3×3) + (5×3)

S3= 9+15

S3 = 24

Therfore s1= a1=8

S2 =a1+a2

16= 8+a2

16-8 = a2

a2 = 8

S3 = a1+ a2+ a3

24 = 8+8+a3

a3 = 24-16

a3 = 8

d = a2-a1

d = 8-8

d =0

Then

Ak = a+ (k-1)×d

164 = 8 + (164-1)×0

164-8= k

K = 156.