Question

the sum of 5th and 7th term of an ap is 52 and the 10th term is 46. find the Ap​

Answer 1

here your answer........

Answer 2

Given :

Sum of 5th term of and 7th term of an AP is 52.

$a_{5}\:+\:a_{7}\:=\:52$

And 10th term is 46.

$a_{10}\:=\:46$

Find :

The AP.

Solution :

According to question,

$\Rightarrow\:a_{5}\:+\:a_{7}\:=\:52$

Now,

$\bold{\boxed{a_{n}\:=\:a\:+\:(n\:-\:1)d}}$

$\Rightarrow\:a\:+\:(5\:-\:1)d\:+\:a\:+\:(7\:-\:1)d\:=\:52$

$\Rightarrow\:a\:+\:4d\:+\:a\:+\:6d\:=\:52$

$\Rightarrow\:2a\:+\:10d\:=\:52$

$\Rightarrow\:a\:+\:5d\:=\:26$

$\Rightarrow\:a\:=\:26\:-\:5d$ ____ (eq 1)

Similarly,

$\Rightarrow\:a_{10}\:=\:46$

$\Rightarrow\:a\:+\:(10\:-\:1)d\:=\:46$

$\Rightarrow\:a\:+\:9d\:=\:46$

$\Rightarrow\:26\:-\:5d\:+\:9d\:=\:46$

[From (eq 1)]

$\Rightarrow\:4d\:=\:20$

$\rightarrow\:d\:=\:5$

Put value of d in (eq 1)

$\Rightarrow\:a\:=\:26\:-\:5(5)$

$\Rightarrow\:a\:=\:26\:-\:25$

$\rightarrow\:a\:=\:1$

So,

AP : a, a + d, a + 2d, a + 3d

• a = 1
• a + d = 1 + 5 = 6
• a + 2d = 1 + 2(5) = 1 + 10 = 11
• a + 3d = 1 + 3(5) = 1 + 15 = 16

∴ AP is 1, 6, 11, 16....