Find the 20th term of ap whose 3rd term is 7and the 7th exceeds 3 times by 2 also find nth term
Answers
a+2d=7............(1)
a7=3(a3)+2
a+6d=3(7)+2
a+6d=23............(2)
BY SUBTRACTING (1) AND (2)
a+2d=7
a+6d=23
-4d=-16
d=16/4
d=4
IF d=4 THEN a=
a+2d=7
a+2(4)=7
a+8=7
a=-1
a20=a+19d
=-1+19(4)
=-1+76
=75
SO, 25th term of an AP is 75
Given,
The third term of the AP (a3) = 7
The 7th term exceeds the 3 times of the third term by 2.
To find,
The 20th and nth terms of the AP.
Solution,
The 20th and nth terms of the AP will be 75 and (4n-5) respectively.
We can easily solve this problem by following the given steps.
According to the question,
The third term of the AP (a3) = 7
We know that the formula to find the nth term of an AP is given as follows:
an = a+(n-1)d where a is the first term, n is the number of the term and d is the common difference.
a3 = a+(3-1)d
a+2d = 7 --- (1)
Now, we have
The 7th term exceeds the 3 times of the third term by 2.
a7 = 3(a3)+2
Putting the value of a3,
a+(7-1)d = 3(7)+2
a+6d = 21+2
a+6d = 23 --- (2)
Subtracting equation (1) from (2),
a+6d-a-2d = 23-7
4d = 16
d = 16/4
d = 4
Putting the value of d in equation (1),
a+2d = 7
a+2(4) = 7
a+8 = 7
a = 7-8
a = -1
Now, the 20th term will be:
a20 = a+(20-1)d
a20 = -1+19(4)
a20 = -1+76
a20 = 75
And the nth term will be:
an = a+(n-1)d
an = -1+(n-1)4
an = -1+4n-4
an = 4n-5
Hence, the 20th term and nth term of the AP will be 75 and (4n-5) respectively.