Question : In an AP if sum of its first n terms is 3n²+5n and its kth term is 164, find the value of k.
Doubt by Saumya
Solution :
Sn=3n²+5n
ak=164
k=?
Sn=3n²+5n
ak=164
k=?
Sn=3n²+5n
S1=a1=3(1)²+5(1)
S1=a1=3+5
S1=a1=8
S1=a1=3(1)²+5(1)
S1=a1=3+5
S1=a1=8
S2=a1+a2=3(2)²+5(2)
S2=a1+a2=3(4)+10
S2=a1+a2=12+10
S2=a1+a2=22
a1+a2=22
8+a2=22
a2=22-8
a2=14
d=a2-a1
d=14-8
d=6
Hence,
a=8
d=6
S2=a1+a2=3(4)+10
S2=a1+a2=12+10
S2=a1+a2=22
a1+a2=22
8+a2=22
a2=22-8
a2=14
d=a2-a1
d=14-8
d=6
Hence,
a=8
d=6
ak=164
a+(k-1)d=164
8+(k-1)6=164
(k-1)6=164-8
(k-1)6=156
k-1=156/6
k-1=26
k=26+1
k=27
a+(k-1)d=164
8+(k-1)6=164
(k-1)6=164-8
(k-1)6=156
k-1=156/6
k-1=26
k=26+1
k=27