Question

In an AP sum of first third term and fifth term 39 and sum of fourth and sixth term is 51 ,find the 10th term of AP

Answer 1

the tenth term of the AP is 60

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

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