Question

the sum of the first 30 terms of an ap is 1920. if the fourth term is 18, find its 11th term

Answer 1

Answer:

46 is the correct answer.

Step-by-step explanation:

Let, first term term is a

and common difference is d.

A/Q,

S30=1920

=>30/2(2a+29d)=1920

=>2a+29d=1920/15

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

Again,

A4=18

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

(2)×2,we get,

2a+6d=36.........................(3)

On (1)-(3), we get,

23d=92

=>d=4

=>a=6

Now, A11=a+10d=6+10×4=6+40=46

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Answer 2

A(11) = 46

Step-by-step explanation:

Given:

S(30) = 1920

A(4) = 18

Find:

A(11)

Computation:

Sn = n/2[2(a) + (n – 1)d]

S(30) = 30/2[2(a) + (30 – 1)d]

1920 = 15[2(a) + 29(d)]

128 = 2(a) + 29(d)  Eq 1

A(4) = 18

18 = a + 3(d)  Eq 2

Eq(2) x 2

So,

2(a) + 6(d) = 36  Eq 3

Eq 3 - Eq 1

d = 4

18 = a + 3(d)

18 = a + 3(4)

a = 6

A(11) = a + 10(d)

A(11) = 6 + 10(4)

A(11) = 46