Question

in a AP the sum of second term fourth term and sixth term is 51 find the 10th term of the sequence ​

Answer 1

Answer:Let the first term be a and the common difference be d

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

⇒ a + ( a + 2d) + (a + 4d) = 39

⇒ a + a + 2d + a + 4d = 39

⇒ 3a + 6d = 39

⇒ a + 2d = 13 --------------------[ 1 ]

The sum of second term, 4th term and 6th term is 51

⇒ ( a + d) + (a + 3d) + (a + 5d) = 51

⇒  a + d + a + 3d + a + 5d = 51

⇒ 3a + 9d = 51

⇒ a + 3d = 17 --------------------[ 2 ]

Put the two equations together:

a + 2d = 13 --------------------[ 1 ]

a + 3d = 17 --------------------[ 2 ]

Equation [ 2 ] - [ 1 ] :

d = 4

Find a:

Sub d = 4  into equation 1

a + 2(4) = 13

a + 8 = 13

a = 5

Form the nth term:

an = a1 + (n - 1)d

an = 5 + (n - 1)4

an = 5 + 4n - 4

an = 4n + 1

Find the 10th term:

an = 4n + 1

a10 = 4(10) + 1

a10 = 41