Advertisements
Advertisements
Question
Find the sum of the two middle most terms of the A.P. `-(4)/(3), -1, -(2)/(3),...,4(1)/(3)`
Solution
A.P. `-(4)/(3), -1, -(2)/(3),...,4(1)/(3)`
Here, `a = -(4)/(3), d = -1 -((-4)/3) -1 + (4)/(3) = (1)/(3)`
l = `4(1)/(3)`
∴ Tn = l = `4(1)/(3) = a + (n - 1)d`
⇒ `4(1)/(3) = (-4)/(3) + (n - 1) xx (1)/(3)`
∴ `(13)/(3) + (4)/(3) = (1)/(3)(n - 1)`
⇒ `(17)/(3) xx (3)/(1)` = (n – 1)
n – 1 = 17
⇒ n = 17 + 1
= 18
∴ Two middle term are `(18)/(2) and (18)/(2) + 1`
= 9th and 10th term
∴ a9 + a10 = a + 8d + a + 9d
= 2a + 17d
= `2 xx ((-4)/3) + 17 xx (1)/(3)`
= `(-8)/(3) + (17)/(3)`
= `(9)/(3)`
= 3.
APPEARS IN
RELATED QUESTIONS
The sum of the 4th and the 8th terms of an A.P. is 24 and the sum of the 6th and the 10th terms of the same A.P. is 34. Find the first three terms of the A.P.
The nth term of a sequence is 8 – 5n. Show that the sequence is an A.P.
For an A.P., show that (m + n)th term + (m – n)th term = 2 × mthterm
The sum of the 4th and the 8th terms of an A.P. is 24 and the sum of the sixth term and the tenth is 44. Find the first three terms of the A.P.
Find the sum of last 8 terms of the A.P. –12, –10, –8, ……, 58.
Find the A.P. whose nth term is 7 – 3K. Also find the 20th term.
Find the 12th from the end of the A.P. – 2, – 4, – 6, …; – 100.
If the seventh term of an A.P. is `(1)/(9)` and its ninth term is `(1)/(7)`, find its 63rd term.
The sum of 5th and 7th terms of an A.P. is 52 and the 10th term is 46. Find the A.P.
If the nth terms of the two A.g.s 9, 7, 5, … and 24, 21, 18, … are the same, find the value of n. Also, find that term
