Sum of first 30 terms of an AP is 1920. If the first term is 18, find the 11th and also the sum of first n terms
Answers
Sum of nth terms of A.P is given by
Sn = (n/2)[2a+(n-1)d]
Where n = Number of terms
a = First term
d = Common difference
n = 30, Sn = 1920
Substitute the values
1920 =(30/2)[2a+29d]
192×2/30 = 2a+29d
128 = 2a+29d
2a+29d=128...................(1)
nth term of an A.P
an = a+(n-1)d
Using the formula
a4 = a+3d = 18
a+3d = 18........................(2)
Equation (2) multiply by 2 and then subtract from equation (1)
23d = 92
d = 92/23
= 4
Substitute the values of d in equation (2)
a+3(4) = 18
a+12 = 18
a = 18-12
= 6
a11 = a+10d
= 6+10(4)
= 46
Hence, the 11th term=46
Sum of first n terms is
Sn = (n/2)[2a+(n-1)d]
Sn = (n/2)[2(6)+(n-1)4]
Sn = n/2[12+4n-4]
Sn = n/2[4n+8]
Sn = n/2[2(2n+4)]
Sn = n(2n+4)
Sn = 2n²+4n
I hope you satisfied with my ANSWER.
Please mark as BRAINLIEST.