please answer this question
Answers
Answer :
25th term , a(25) = -7
Note :
★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.
★ If a1 , a2 , a3 , . . . , an are in AP , then
a2 - a1 = a3 - a2 = a4 - a3 = . . .
★ The common difference of an AP is given by ; d = a(n) - a(n-1) .
★ The nth term of an AP is given by ;
a(n) = a + (n - 1)d .
Solution :
• Given AP : 5 , 4½ , 4 , 3½ , . . .
• To find : 25th term , a(25) = ?
Here , we have ;
• First term , a = 5
• Common difference , d = 4½ - 5
d = 9/2 - 5
d = (9 - 10)/2
d = -½
• n = 25
Now ,
We know that , the nth term of an AP is given as ; a(n) = a + (n - 1)d .
Thus ,
The 25th term of the given AP will be given as ;
=> a(25) = a + (25 - 1)d
=> a(25) = a + 24d
=> a(25) = 5 + 24×(-½)
=> a(25) = 5 - 24/2
=> a(25) = 5 - 12
=> a(25) = -7
Hence ,
The 25th term of the given AP is -7 .
Answer:
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