Math, asked by tanya7955, 1 year ago

The sum of the first 30 terms of an A.P. is 1920. If the fourth term is 18,
find its 11th term. ​

Answers

Answered by lublana
6

The 11th term of an A.P=46

Step-by-step explanation:

Sum of nth terms of A.P is given by

S_n=\frac{n}{2}(2a+(n-1)d)

Where n=Number of terms

a=First term

d=Common difference

n=30, S_n=1920

Substitute the values

1920=\frac{30}{2}(2a+29d)

2a+29d=\frac{1920\times 2}{30}=128

2a+29d=128....(1)

nth term of an A.P

a_n=a+(n-1)d

Using the formula

a_4=a+3d=18

a+3d=18...(2)

Equation (2) multiply by 2 and then  subtract from equation (1)

23d=92

d=\frac{92}{23}=4

Substitute the values of d in equation (2)

a+3(4)=18

a+12=18

a=18-12=6

a_{11}=a+10d=6+10(4)=46

Hence, the 11th term=46

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