Question

The first term of an ap is20 and sum of first seven terms is2100 find 31 term of AP

Answer 1

Answer:

sum of first seven nos in AP=n/2(2a+(n-1)d

2100=7/2(2*20+(7-1)d)

2100=7/2(40+6d)

40+6d=2100*2/7

40+6d=600

6d=600-40=560

d=560/6=280/3

31st term=a+,(n-1)d

20+(31-1)280/3

20+30*280/3

20+2800

2820

Answer 2

The 31 st term of an A.P is 2820.

Step-by-step explanation:

Given : The first term of an AP is 20 and sum of first seven terms is 2100.

To find : 31st term of AP ?

Solution :

The nth term of A.P is $a_n=a+(n-1)d$

The first term is a=20

The sum of first seven terms is 2100.

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

$S_7=\frac{7}{2}(2a+(7-1)d)$

$2100=\frac{7}{2}(2(20)+6d)$

$2100=\frac{7}{2}(40+6d)$

$2100=7(20+3d)$

$2100=140+21d$

$21d=1960$

$d=\frac{1960}{21}$

$d=\frac{280}{3}$

Now, the 31st term of A.P is

$a_{31}=a+30d$

$a_{31}=20+30(\frac{280}{3})$

$a_{31}=20+2800$

$a_{31}=2820$

The 31 st term of an A.P is 2820.

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