Question

The fifth term of an ap is 26 and its tenth term is 51 find ap

Answer 1

Correct Question:-

The 5th Term of an A.P is 26 and it's 10th Term is 51. Find the A.P..

AnswEr:-

AP is 11, 16 , 21..

Step by Step Explanation :-

Given :-

• $\sf \; a5 = 26$
• $\sf\; a10 = 51$

Now,

a + 4d = 26 _____eq(1)

a + 9d = 51 ______eq(2)

From equations (1) & (2)

$:\implies\sf\; a + 4d = 26 = a + 9d = 51$

$:\implies\sf\; d = \dfrac{5}{25}$

$:\implies\sf\; d = 5$

$\rule{150}2$

Now, Putting the value of d in equation (1) we get,

$:\implies\sf\; a + 4d = 26$

$:\implies\sf\; a + 4(5) = 26$

$:\implies\sf\; a + 20 = 26$

$:\implies\sf\; a = 26 - 20$

$:\implies\sf\; a = 6$

$\rule{150}2$

Now,

a + d

$:\implies\sf\; 6 + 5$

$:\implies\sf\; 11$

a + 2d

$:\implies\sf\; a +2(5)$

$:\implies\sf\; 6 + 10$

$:\implies\sf\; 16$

a + 3d

$:\implies\sf\; a +3(5)$

$:\implies\sf\; 6 + 15$

$:\implies\sf\; 21$

So, The A.P is 11, 16 , 12.

$\rule{150}2$

Answer 2

Answer:

AP: 6, 11, 16....

Step-by-step explanation:

Given:

Fifth term (a₅) = 26

Tenth term (a₁₀) = 51

To find: AP

Solution:

We know that An = a + (n-1) d

where, An = nth term

a = first term of the AP

n = Total number of term(s) in the AP

d = Common difference

a₅ = a + 4d

=> a + 4d = a₅

=> a + 4d = 26 ---> (1)

a₁₀ = a + 9d

=> a + 9d = a₁₀

=> a + 9d = 51 ---> (2)

Subtracting (1) from (2) we get:

a + 9d = 51

a + 4d = 26

———————

5d = 25

=> d = 25/5

=> d = 5

Putting the value of 'd' in (1) :

a + 4d = 26

=> a + 4(5) = 26

=> a + 20 = 26

=> a = 26 - 20

=> a = 6 {first term}

Now, a₂ = a + d

=> a₂ = 6 + 5

=> a₂ = 11 {second term}

a₃ = a + 2d

=> a₃ = 6 + 2(5)

=> a₃ = 6 + 10

=> a₃ = 16 {third term}

∴ The AP is 6, 11, 16...