Find the 9th term of an arithmetic sequence with 4th term 10 and common difference 6
Answers
Answer:
It is easy
Step-by-step explanation:
Topic
Arithmetic Progression
Given
4^{th}4th term of an Arithmetic Progression is 14 and 9^{th}9th term is 29.
To Find
The common difference and
First Term of AP.
Concept Used
n^{th}nth term of an AP is given by :-
a_n = a + ( n - 1 )dan=a+(n−1)d
where
a = First term of AP
n = Number of term
d = Common Difference
Solution
It is given that 4^{th}4th term of AP is 14.
a_{4}=a+(4-1)da4=a+(4−1)d
14=a+3d14=a+3d
Now,
It is given that 9^{th}9th term of AP is 29.
a_{9}=a+(9-1)da9=a+(9−1)d
29=a+8d29=a+8d
We need to solve these two obtained equations.
Subtracting equation (1) from equation (2),
(a+8d)-(a+3d)=29-14(a+8d)−(a+3d)=29−14
a+8d-a-3d=29-14a+8d−a−3d=29−14
a-a+8d-3d=29-14a−a+8d−3d=29−14
5d=155d=15
d=\dfrac{15}{5}d=515
d=3d=3
Now, put value of 'd' in any obtained equation.
a + 3d = 14
a + 3(3) = 14
a + 9 = 14
a = 14 - 9
a = 5
So, a = 5 and d = 3.
Answer
The first term of AP is 5 and common difference of AP is 3.
I hope it is helpful for you