In an AP:
Given $d = 5, S_9 = 75$, find $a$ and $a_9$.
Given:
In an A.P., $d = 5, S_9 = 75$
To do:
We have to find $a$ and $a_9$.
Solution:
We know that,
$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$
$S_{9}=\frac{9}{2}[2 a+(9-1) d]$
$75=\frac{9}{2}[2 a+8 d]$
$75 \times \frac{2}{9}=2a+8(5)$
$\frac{50}{3}=2 a+40$
$2a=\frac{50}{3}-40$
$2a=\frac{50-120}{3}$
$2a=\frac{-70}{3}$
$a=\frac{-35}{3}$
$a_{9}=a+8 d$
$=\frac{-35}{3}+8(5)$
$=\frac{-35}{3}+40$
$=\frac{-35+120}{3}$
$=\frac{85}{3}$
Related Articles
- In an AP:Given $a = 7, a_{13} = 35$, find $d$ and $S_{13}$.
- In an AP:Given $a_{12} = 37, d = 3$, find $a$ and $S_{12}$.
- In an AP:Given $a = 2, d = 8, S_n = 90$, find $n$ and $a_n$.
- In an AP:Given $a = 8, a_n = 62, S_n = 210$, find $n$ and $d$.
- In an AP:Given $a_n = 4, d = 2, S_n = -14$, find $n$ and $a$.
- In an AP:Given $a = 3, n = 8, S = 192$, find $d$.
- In an AP:Given $a_3 = 15, S_{10} = 125$, find $d$ and $a_{10}$.
- In an AP:Given $l = 28, S = 144$, and there are total 9 terms. Find $a$.
- Find the L.C.M of 30 and 75.
- In an AP:(i) given \( a=5, d=3, a_{n}=50 \), find \( n \) and \( S_{n^{\circ}} \).(ii) given \( a=7, a_{13}=35 \), find \( d \) and \( \mathrm{S}_{13} \).(iii) given \( a_{12}=37, d=3 \), find \( a \) and \( \mathrm{S}_{12} \).(iv) given \( a_{3}=15, \mathrm{~S}_{10}=125 \), find \( d \) and \( a_{10} \)(v) given \( d=5, \mathrm{~S}_{9}=75 \), find \( a \) and \( a_{9} \).(vi) given \( a=2, d=8, \mathrm{~S}_{n}=90 \), find \( n \) and \( a_{n} \)(vii) given \( a=8, a_{n}=62, \mathrm{~S}_{\mathrm{n}}=210 \), find \( n \) and \( d \).(viii) given \( a_{n}=4, d=2, \mathrm{~S}_{n}=-14 \), find \( n \) and \( a \).(ix) given \( a=3, n=8, \mathrm{~S}=192 \), find \( d \).(x) given \( l=28, S=144 \), and there are total 9 terms. Find \( a \).
- Express as rupees using decimals:(a) 5 paise(b) 75 paise
- What are the common factors of 75, 60 and 90?A) 1, 2, 3, 5 and 6B) 1, 3, 5 and 10C) 1, 2, 5 and 7D) 1, 3, 5 and 15
- Find four elements a, b, c and d in an array such that a+b = c+d in C++
- 75% of a number is 9.7. Find the number.
Kickstart Your Career
Get certified by completing the course
Get Started