Advertisements
Advertisements
Question
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
Advertisements
Solution
d = 5, S9 = 75
an = a + (n – 1)d
a9 = a + (9 – 1) x 5
= a + 40 ...(i)
S9 = `n/(2)[2a + (n - 1)d]`
75 = `(9)/(2)[2a + 8 xx 5]`
`(150)/(9)` = 2a + 40
2a = `(150)/(9) - 40`
= `(50)/(3) - 40`
2a = `(-70)/(3)`
⇒ a = `(-70)/(2 xx 3)`
a = `(-35)/(3)`
From (i),
a9 = a + 40
= `(-35)/(3) + 40`
= `(-35 + 120)/(3)`
= `(85)/(3)`
∴ a = `(-35)/(3), a_9 = (85)/(3)`.
APPEARS IN
RELATED QUESTIONS
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Which term of the A.P. 121, 117, 113, ... is its first negative term?
[Hint: Find n for an < 0]
Find the sum of the following arithmetic progressions:
–26, –24, –22,... to 36 terms
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Write an A.P. whose first term is a and common difference is d in the following.
a = 6, d = –3
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 – S10).
x is nth term of the given A.P. an = x find x .
The sum of all two digit odd numbers is ______.
