Question

the sum of the first third term of an ap is 39 and the sum if second fourth and sixth term is 51 then find the 10 th term of ap

Answer 1

Sorry for the mess...

Hope this could be the answer...let me know about that... :-)

Answer 2

Answer:

Step-by-step explanation:

Given; The sum of first term, third term and fifth term is 39 & the sum of second, fourth and sixth terms is 51

To find: The 10th term of the A.P

Solution:

The sum of first term, third term and fifth term is 39

i.e. Let the first term be ' a '

Third term be ' a + 2d '

Fifth term be ' a + 4d '

Sum = 39 ( given )

→ a + a + 2d + a + 4d = 39

→ 3a + 6d = 39

→ 3 ( a + 2d ) = 39

→ a + 2d = 13 -----[1]

The sum of second, fourth and sixth terms is 51

Let the second term be ' a + d '

Fourth term be ' a + 3d '

Sixth term be ' a + 5d '

Sum = 51 ( given )

→ a + d + a + 3d + a + 5d = 51

→ 3a + 9d = 51

→ 3 ( a + 3d ) = 51

→ a + 3d = 17 -----[2]

Solve equation [1] & [2]

We get,

$a + 2d = 13 \: -----[1]\\\underline{a + 3d = 17} \: -----[2]\\-d = -4$

$\underline{\boxed{\bold{D = 4}}}$

Substitute 'd' in [1] or [2]

→ a + 3d = 17

→ a + 12 = 17

→ a = 17 - 12 = 5

10'th term = a + 9d

→ a + 9d

→ 5 + 36 = 41

⇒ a₁₀ 41

$\underline{\boxed{\bold{a_{10} = 41}}}$