Question

If the 8th and 14th terms of an A.P. be 39 and 69 respectively, then its 69th term will be

Answer 1

Given:

If the 8th and 14th terms of an A.P. be 39 and 69 respectively

To find:

Its 69th term will be?

Solution:

We know the nth term of an A.P. is given as:

$\boxed{\bold{T_n = a + (n-1)d}}\\\Rightarrow where \:T_n = nth \:term, a = first\:term \:\&\: d = common\:difference}$

So, using the above formula we will find the expression for the 8th term and the 14th term of the A.P.:

$T_8 = 39$

$\implies a + (8-1)d= 39$

$\implies a + 7d= 39$ ...... (i)

and

$T_1_4 = 69$

$\implies a + (14-1)d= 69$

$\implies a + 13d= 69$ ...... (ii)

Subtracting (i) from (ii), we get

a + 13d = 69

a + 7d =  39

-   -         -

--------------------

   6d = 30

--------------------

∴ d = $\frac{30}{6} = \bold{5}$

Substituting the value of "d" in eq. (i), we get

a + (7× 5) = 39

⇒ a + 35 = 39

⇒ a = 39 - 35

⇒ a = 4

Now, by substituting the values of "a= 4" & "d = 5", we will find the value of 69th term of the A.P.:

T₆₉ = 4 + (69 - 1)5 = 4 + (68 × 5) = 4 + 340 = 344

Thus, its 69th term will be → 344.

-----------------------------------------------------------------------------------

Also View:

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is Zero?

https://brainly.in/question/107286

find the 60th term of the AP 8,10,12, if it has a total of 60 terms and hence find the sum of its last ten terms?

https://brainly.in/question/304224

The 8th term of an A.P is 17 and 19th term is 39 find the common difference​

https://brainly.in/question/15762324

Answer 2

Answer:

Step-by-step explanation:

Given:

If the 8th and 14th terms of an A.P. be 39 and 69 respectively

To find:

Its 69th term will be?

Solution:

We know the nth term of an A.P. is given as:

So, using the above formula we will find the expression for the 8th term and the 14th term of the A.P.:

...... (i)

and

...... (ii)

Subtracting (i) from (ii), we get

a + 13d = 69

a + 7d =  39

-   -         -

--------------------

  6d = 30

--------------------

∴ d =  

Substituting the value of "d" in eq. (i), we get

a + (7× 5) = 39

⇒ a + 35 = 39

⇒ a = 39 - 35

⇒ a = 4

Now, by substituting the values of "a= 4" & "d = 5", we will find the value of 69th term of the A.P.:

T₆₉ = 4 + (69 - 1)5 = 4 + (68 × 5) = 4 + 340 = 344

Thus, its 69th term will be → 344.

hope it helps you