Question

in an ap if first n term is 3 n square + 5n and its kth term is 164 find the value of k

Answer 1

Answer:

3n^2 + 5n

when n is 1

3 x [1]^2 + 5 x 1=8

when n is 2

3 x [2]^2 + 5 x 2=22

when n is 3

3 x [3]^2 + 5 x 3=42

S1=a1

therefore a is 8.

a2= S2-a1=22-8=14

a1=8 and a2=14

therefore d is a2-a1=14-8=6.

therefore the AP is 8,14,20..........

we know that an=a +[n-1]d,

given 164 is the ak

so,164= 8 +[k-1]6

164-8=6k-6

156+6=6k

162/6=k

k=27