Question

The fifth term of an A.P is 20 and the sum of its seventh and eleventh terms is 64. Find the common difference.

Answer 1

Answer:         a5 = 20

               a + 4d = 20 ------- (1)

             a7 + a11 = 64        

a + 6d + a + 10d = 64

           2a + 16d = 64

               a + 8d = 32 -------(2)

From 1 - 2

                    -4d = -12

                       d = 3

                        ====

           

Step-by-step explanation:

Answer 2

$\huge\sf\pink{Answer}$

☞ Common Difference of AP is 3

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Fifth term of AP , a₅ = 20

✭ Sum of seventh and eleventh term of AP is 64 , a₇ + a₁₁ = 64

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The Common Difference?

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\bullet\:\underline{\textsf{As Per the Question}}$

➝ $\sf a_5 = 20$

➝ $\sf a + 4 d = 20$

➝ $\sf a = 20 - 4 d\qquad -eq(1)$

And also,

➢ $\sf a_7 + a_{11}=64$

➢ $\sf a+6d+a+10d=64$

➢ $\sf 2a+16d = 64$

From eq(1) we get,

»» $\sf 2( 20-4d)+16d=64$

»» $\sf 40 - 8d + 16d = 64$

»» $\sf 8d + 40 = 64$

»» $\sf 8d = 64 - 40$

»» $\sf 8d = 24$

»» $\sf d = \dfrac{24}{8}$

»» $\sf\orange{d = 3}$

$\rule{170}3$