Question

Find the 3 terms of an A.P in which sum of first two terms is 10 and the sum of last two terms is 16

Answer 1

Answer:

Correct option is A)

Hint:- The sum formula for n terms of an A.P. (

2

n

{2a+(n−1)d}) will be used along with the related terms.

Given:-

Sequence: 10,6,2,...

a=10=first term

n=16=no. of terms

Step 1: Finding the common difference 'd' of the given sequence 10,6,2,....

second term − first term =a

2

−a

1

=6−10=−4

third term − second term =a

3

−a

2

=2−6=−4

As the difference is same in all the cases, hence it's common difference=d=−4

Answer 2

The value of 3 terms of an A.P  are 3.5 , 6.5 and 9.5.

Step-by-step explanation:

Given:

First two terms sum  is 10.

Last two terms sum is 16,

To Find:

The value of 3 terms of an A.P.

Formula Used:

nth term of the Arithmetic Progression (A.P) tn= y+(n-1)z       ---------------------- formula no.01.

Where

y = first term

z =   common difference.

n =  number of the  terms

tn =  nth term of the Arithmetic Progression (A.P)

Solution:

Let the three terms of an Arithmetic Progression (A.P) are y-z, y and y+z

Where y = first term    and z =   common difference.

As given- first two terms sum  is 10.

$y-z+y=10$

$2y-z=10$  ------------------------- equation no.01

As given- last two terms sum is 16,

$y+y+z=16$

$2y+z=16$ ------------------------equation no.02

Adding equation 01  with equation no.02 , we get.

$4y=26$

$y=6.5$

Putting value of y  = 6.5 in equation 01, we get.

$2\times 6.5-z=10$

$z=13-10$

$z=3$

First term of A .P. $=y-z=6.5-3$

                                          $=3.5$

Second  term of A .P.  $=y=6.5$

Third term of  A.P. $= y+z= 6.5+3$

                                            $=9.5$

Thus,  The value of 3 terms of an A.P  are 3.5  ,  6.5  and 9.5.