Question

the
fifth term of
Ap is 26 and its tenth
term is 51 find Ap​

Answer 1

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Answer 2

$\huge\underline\mathrm{Question-}$

The fifth term of Ap is 26 and its tenth term is 51. find Ap.

$\huge\underline\mathrm{Solution-}$

Given :

• $a_5$ = 26
• $a_{10}$ = 51

To find :

• Arithmetic progression

Explanation :

★ $a_5$ = 26 [ given ]

$\mapsto$ a + 4d = 26 _______(1)

★ $a_{10}$ = 51

$\mapsto$ a + 9d = 51 _______(2)

Subtract eq (2) from (1),

We get,

$\mapsto$ -5d = -25

$\mapsto$ d = $\cancel{\dfrac{-25}{-5}}$

$\huge{\boxed{\red{\mathrm{d=5}}}}$

Now, put d = 5 in eq (1)

$\mapsto$ a + 4(5) = 26

$\mapsto$ a + 20 = 26

$\mapsto$ a = 26 - 20

$\huge{\boxed{\red{\mathrm{a=6}}}}$

$\rule{200}1$

Here, first term = a => 6

Second term = a + d => 6 + 5 = 11

Third term = a + 2d => 6 + 2(5) = 16

$\large{\boxed{AP-\:6,11,16...}}$