7th term is 34,15th term is 66 what is the common difference? find the 20th term
Answers
Consider an arithmetic sequence whose 7th term is 34 and the 15th terms are 66. What is the common difference and what is the 20th term?
To answer this question, we will build two equations with two unknowns, using
a(n) = a(1) + (n-1)d
so,
34 = a(1) + 6d
66 = a(1) +14d
Using elimination by multiply the first term by -1, we get:
-34 = -a(1) -6d
66 = a(1) + 14d
which becomes,
32 = 8d
d = 4
plugging that difference into the first equation, we get
34 = a(1) +6(4)
a(1) = 10
Since we know now know the difference and the first term, we use the first equation is get the 20th term.
a(20) = 10 + (20–1)4
a(20) = 86.
So, the answers to this problem are 4 for the difference, and 86 for the 20th terms.
Step-by-step explanation:
Given :-
7th term = 34,
15th term = 66
To find :-
What is the common difference?
Find the 20th term ?
Solution :-
We know that
The general term of an AP = an = a+(n-1)d
Where , a = First term
d = Common difference
n = Number of terms
Given that :
7th term = 34
=> a7 = 34
=> a+(7-1)d = 34
=> a+6d = 34 --------------(1)
15th term = 66
=> a15 = 66
=> a+(15-1)d = 66
=> a+14d = 66 -------------(2)
On subtracting (1) from (2) then
a + 14d = 66
a + 6d = 34
(-)
_________
0 + 8d = 32
_________
=> 8d = 32
=> d = 32/8
=> d = 4
Common difference = 4
Now
on Substituting the value of d in (1) then
=> a +6(4) = 34
=> a +24 = 34
=> a = 34-24
=> a = 10
First term = 10
Now ,
20th term = a 20
=> a+(20-1)d
=> a+19d
=> 10+19(4)
=> 10+76
=> 86
Therefore, a 20 = 86
Answer:-
The Common difference is 4
20th term of the given AP = 86
Used formulae:-
The general term of an AP = an = a+(n-1)d
Where , a = First term
d = Common difference
n = Number of terms