Question

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

Answer 1

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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