Question

Five terms are in AP. The difference between the square of the 5th term and first term is
and the sum of 2nd and the 4th term is 16. Find the first 5 terms.​

Answer 1

Answer:

Read the question.....it is incomplete here

Five terms are in AP.The difference between the square of the 5th term and the first is______???.and the sum of 2nd and the 4th term is 16.Find the first 5 terms please see to it.

Answer 2

7.50,7.75,8.00,8.25.8.50

Step-by-step explanation:

Given,

Let the five terms of AP is

$a_{1},a_{2},a_{3},a_{4},a_{5}$

a is the first term and d is the common difference

$a,a+d,a+2d,a+3d,a+4d$

$\left ( a_{5} \right )^{2}-\left ( a_{1} \right )^{2}=16$

$a_{2}+a_{4}=16$

Solution,

$a_{2}+a_{4}=16$

$a+d+a+3d=16$

$2a+4d=16$                 (1)

$a+2d=8$                      (2)

$\left ( a_{5} \right )^{2}-\left ( a_{1} \right )^{2}=16$

$\left ( a+4d \right )^{2}-\left ( a \right )^{2}=16$

$\left ( a+4d+a \right )\left ( a+4d-a \right )=16$          ((a²-b²)=(a+b)(a-b))

$\left ( 2a+4d \right )\left ( 4d \right )=16$

$16\times 4d=16$                     (put the value of $2a+4d$=16 from equation (1))

$4d=1$

$d=1/4$

$a+2d=8$                        (from equation 2)

$a=8-2\times 1/4=15/2=7.50$

$a_{1}=a=15/2=7.50$

$a_{2}=a+d=15/2+1/4=31/4=7.75$

$a_{3}=a+2d=15/2+2\times 1/4=16/2=8$

$a_{4}=a+3d=15/2+3\times 1/4=33/4=8.25$

$a_{5}=a+4d=15/2+4\times 1/4=17/2=8.50$