Question

In an arthemetic progression sum of 3rd and 7thterm is 6. And that product of 3rd and 7th term is 8. Then write arthemetic progression .​

Answer 1

hope you've got It

mark as brainliest please

Answer 2

Given:-

• Sum of 3rd and 7th term = 6.

• Product of 3rd and 7th term = 8.

To Find:-

• Arithmetic Progression

Formula used:-

• $a_n=a+(n-1)d$

Solution:-

According to question,

$\implies\:a_3+a_7=6$

$\implies\:a+(3-1)d+a+(7-1)d=6$

$\implies\:2a+2d+6d=6$

$\implies\:2a+8d=6$

$\implies\:a+4d=\dfrac{6}{2}$

$\implies\:a+4d=3$

$\implies\:a=3-4d$ ____{1}

Also,

$\implies\:a_3\times\:a_7=8$

$\implies\:(a+2d)(a+6d)=8$

$\implies\:(3-4d+2d)(3-4d+6d)=8$ {from 1}

$\implies\:(3-2d)(3+2d)=8$

$\implies\:3^2-(2d)^2=8$

$\implies\:9-4d^2=8$

$\implies\:4d^2=9-8$

$\implies\:d^2=\dfrac{1}{4}$

$\implies\:d=\sqrt{\dfrac{1}{4}}$

$\implies\:d=±\dfrac{1}{2}$

When d =$\dfrac{1}{2}$

$a=3−4d=3−4×\dfrac{1}{2}=3-2=1$

When d = $-\dfrac{1}{2}$

$a=3−4d=3−4×-\dfrac{1}{2}=3+2=5$

When a = 1 and d = ½ then A.P is,

• a = 1
• a + d = 1 + ½ = 1.5
• a + 2d = 1 + 2×½ = 2
• a + 3d = 1 + 3×½ = 2.5

1, 1.5, 2, 2.5, . . . .

When a = 5 and d = -½ then A.P is,

• a = 5
• a + d = 5 - ½ = 4.5
• a + 2d = 5 - 2×½ = 4
• a + 3d = 5 - 3×½ = 3.5

5, 4.5, 4, 3.5, . . . .

Hence, the A.P will either 1, 1.5, 2, 2.5, . . . . or 5, 4.5, 4, 3.5, . . . .

━━━━━━━━━━━━━━━━━━━━━━━━━