If frist term. Of. An. AP. is. 10 and. 25th. Term is.130 findThe 13th term
Answers
Given:
In an arithmetic progression, the first term is ten.
The twenty-fifth term of the arithmetic progression is 130.
To find:
The value of the thirteenth term of an A.P.
Solution:
In an arithmetic progression, the difference between consecutive terms of the series gives a common difference, denoted by d.
The formula for finding the nth term of an A.P. is,
an = a + (n-1) d
(a) = first term
d = common difference
The 25th term is 130.
The first term is 10.
a₂₅ = 10 + (25-1) d ( n= 25)
10 + 24d = 130 (equation 1)
From equation 1, we can calculate the value of the common difference d.
24d = 130 – 10
24d = 120
d = 120/24
d = 5
The common difference d is 5.
The thirteenth term is,
A₁₃ = 10 + (13 -1) d (n=13)
10 + 12d = a₁₃ (equation 2)
Putting the value of d =5 in equation 2, we will get the value of the 13th term.
10 + (12×5)= a₁₃
a₁₃ = 70
The thirteenth term of the A.P is 70.