Question

In an A.P, the 5th and 11th term are 7 and 10 respectively. Then, the value of the 100th term is​

Answer 1

Step-by-step explanation:

T5 = 7

T11= 10

Since we know that Tn= a+(n-1)d

Therefore ,

T5 = a+(5-1)d

7= a+ 4d -------------( 1 )

T11= a+(11-1)d

10= a+ 10d ---------------( 2 )

Solving equations 1 and 2 , we get ,

d=1/2

Since, we now have the value of d

putting the value of d in the equation 2

10 = a + 10 * 1/2

a = 5

T100 = a + ( 100 - 1 ) d

T100 = 5 + 99 * 1/2

T100 = 5+ 49.5

T100 = 54.5

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Answer 2

The 100th term of an A. P. is 54.5

Step-by-step explanation:

GIVEN

5th term = 7

11th term = 10

___________________________

To Find

value of the 100th term

___________________________

Let (a) be the first term and (d) the common difference

We know that,

tn = a + ( n - 1 ) d

∴ tn = a + ( 5 - 1) d

∴ 7 = a + 4d ..... (1)

and

t10 = a + ( 11 - 1) d

∴ 10 = a + 10d ..... (2)

Now,

Subtracting equation (1) from equation (2)

10 = a + 10d .....(2)

7 = a + 4d .....(1)

- - -

__________

3 = 6d

∴ d = 3 / 6

∴ d = ½

Now,

Substituting d = ½ in equation (1)

7 = a + 4 × ½

∴ 7 = a + 2

∴ a = 7 - 2

∴ a = 5

Now,

t100 = a + ( 100 - 1 ) d

= 5 + 99 × ½

= 5 + 49.5

= 54.5

∴ t100 = 54.5

The 100th term of an A. P. is 54.5