Question

Find the five terms of an A.P. whose sum is 25/2 and first and last term ratio is 2 : 3.

Answer 1

Answer:

an=a+n-1d

an=5

an=259kk for have ham log use today kar ehae he na

Answer 2

The five terms of an Arithmetic progression is 2, 2.25 , 2.50 , 2.75 , 3  

Step-by-step explanation:

Given as :

The sum of five terms of an Arithmetic progression = $\dfrac{25}{2}$

i.e    $S_5$ = $\dfrac{25}{2}$

The ratio of first term to last term = 2 : 3

Let The first term = 2 x

Let The last term = 3 x

According to question

Since, Sum of n term of an A.P = $S_n$ = $\dfrac{n}{2}$ [ first term  + last term ]

Or, $S_n$ = $\dfrac{n}{2}$ [ first term  + last term ]

Now, for n = 5

$S_5$ = $\dfrac{5}{2}$  × [ 2 x + 3 x ]

Or, $\dfrac{25}{2}$  = $\dfrac{5}{2}$  ×  5 x

Or,  $\dfrac{25x}{2}$ = $\dfrac{25}{2}$

from cross multiplication

 25 x × 2 = 25 × 2

Or, 50 x = 50

∴         x = $\dfrac{50}{50}$

i.e       x = 1

So, The first term =  2 × 1 = 2

And The last term = 3 × 1 = 3

So, The first term = 2

     The second term = 2.25

    The third term = 2.50

     The fourth term = 2.75

      The fifth term = 3

Hence, The five terms of an Arithmetic progression is 2, 2.25 , 2.50 , 2.75 , 3  Answer