Question

The sum of first n terms of an



a.P is 5n square +3n if it's mth term is 168, find the value of m also find the 20th term of the



a.P

Answer 1

Given: Sum of first n terms of a.p is
5n^2 +2 and m th term is 168.
To find: Find the 20th term.
Solution: We have given that
Sn= 5n^2 + 3n.
For n=1
S1= 5(1)^2 + 3(1)
S1= 5 + 3 = 8
S1= 8
For n=2
S2=5(2)^2+ 3(2)
S2=5(4)+6
S2=26
By the formula:
Sn=n/2{2a+(n-1)d}
Where, a= first term
d=common difference
For n=2
S2=2/2(2a+d)
Plug the value of S2= 26, a=8
26= 1 (2*8+d)
26= 16+d
Switch the sides and subtract both side by 16
d=10
For mth term.
168= 8+(m-1)10
168-8= (m-1)10
160= (m-1)10
On dividing both sides by 10
160/10 =(m-1)
16= (m-1)
On adding bith sides by 1
16+1= m
m=17
Now, we need to find a20.
a20= a+(20-1)d
Plug the value a=8, d= 10
a20= 8+(19)10
a20= 8+190
a20= 198.
Therefore, m=17, a20= 198.