The sum of 4 th and 8th term is 24 and the sum of 6th and 10 th term i

1.	The sum of 4 th and 8th term is 24 and the sum of 6th and 10 th term is 44 .Find AP
Answer» Let the first term and the common difference of the AP be a and d respectively.Then,4th term = a + (4 - 1)d = a + 3d\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}8th term = a + (8 - 1)d = a + 7d\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}6th term = a + (6 - 1)d = a + 5d\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}and 10th term = a + (10 - 1)d = a + 9d\xa0{tex}\\because {a_n} = a + (n - 1)d{/tex}According to the question,4th term + 8th term = 24{tex} \\Rightarrow {/tex}\xa0(a + 3d) + (a + 7d) = 24{tex} \\Rightarrow {/tex}\xa02a + 10d = 24{tex} \\Rightarrow {/tex}\xa0a + 5d = 12 .......... (1) (Dividing throughout by 2)6th term + 10th term = 24{tex} \\Rightarrow {/tex}\xa0(a + 5d) + (a + 9d) = 44{tex} \\Rightarrow {/tex}\xa02a + 14d = 44{tex} \\Rightarrow {/tex}\xa0a + 7d = 22 .......... (2) (Dividing throughout by 2)Solving (1) and (2), we geta = -13d = 15So, First term = -13Second term = -13 + 5 = -8Third term = -8 + 5 = -3Hence, the first three terms of the given AP are -13, -8 and -3.

The sum of 4 th and 8th term is 24 and the sum of 6th and 10 th term is 44 .Find AP