If the 6 term of an ap is11 and the last term is 9 ,find the number of term if the common difference is 3/2
We can use the formula for the nth term of an arithmetic progression (AP):
An = A1 + (n-1)d
Where An is the nth term, A1 is the first term, n is the number of terms, and d is the common difference.
Given that the 6th term (A6) is 11, the last term (An) is 9, and the common difference (d) is 3/2, we can set up the following equations:
A6 = A1 + (6-1)d
11 = A1 + 5(3/2)
11 = A1 + 15/2
An = A1 + (n-1)d
9 = A1 + (n-1)(3/2)
Now we can solve these equations simultaneously.
From the first equation:
11 = A1 + 15/2
A1 = 11 - 15/2
A1 = 11/2 - 15/2
A1 = -4/2
A1 = -2
Substituting A1 = -2 into the second equation:
9 = -2 + (n-1)(3/2)
9 + 2 = (n-1)(3/2)
11 = 3n/2 - 3/2
11 + 3/2 = 3n/2
25/2 = 3n/2
Multiplying both sides by 2/3:
(25/2)(2/3) = n
25/3 = n
Therefore, the number of terms in the arithmetic progression is 25/3 or 8.33 (rounded to the nearest whole number).
Note: It's important to note that the number of terms in an arithmetic progression should be a whole number, so in this case, we can round up to the nearest whole number to get 9 terms.