In an ap the sum of the first four terms is 20 and the sum of first three terms is 12 then find the fourth term of the ap
Answers
Answer:
2, 4, 6, 8
Step-by-step explanation:
suppose 4 terms of A.P. be ( a - d ), a ,a+d, a+2d
first condition
a-d+a+a+d+a+2d = 20
4a+2d =20
Dividing both side by 2
2a+d = 10.......1
Second condition
a-d+a+a+d = 12
3a =12
a =4
put a =4 in 1
2a+ d = 10
8 +d = 10
d = 10 -8
d = 2
Here, a =4 , d = 2
The 4 terms are
1) a -d = 4 -2 =2
2) a = 4
3) a+d = 4+2 = 6
4) a+2d = 4 + 4 = 8
Given,
The sum of the first 4 terms of an AP = 20
The sum of the first three terms = 12
To find,
The 4th term of the AP.
Solution,
We can easily solve this problem by following the given steps.
According to the question,
We have:
The sum of the first 4 terms of an AP = 20
The sum of the first three terms = 12
We know that in an AP we obtain the next term by adding the common difference(d) to the previous term.
Or the formula to find the nth term is:
an = a+(n-1)d where a is the first term and n is the number of the term
So,
a1 = a
a2 = a+d
a3 = a+2d
a4 = a+3d
Adding these four terms:
a+a+d+a+2d+a+3d = 20
4a+6d = 20
Taking 2 as a common factor:
2(2a+3d) = 20
2a+3d = 20/2
2a+3d = 10 ---(1)
Now,
Add the first three terms:
a+a+d+a+2d = 12
3a+3d = 12
Taking 3 as a common factor:
3(a+d) = 12
a+d = 12/3
a+d = 4
a = (4-d) ---(2)
Putting this value in equation (1),
2(4-d)+3d = 10
8-2d+3d = 10
8+d = 10
d = 10-8
d = 2
Put this value in equation 2,
a = 4-2
a = 2
Now, we know that:
a4 = a+3d
Put the values of a and d:
a4 = 2+3(2)
a4 = 2+6
a4 = 8
Hence, the 4th term of the AP is 8.