Find how many terms has an a.p whose common diffrence and first term are respectively negetive 6 and 8 and the last term is 82.
How many terms has an A.P, who the common difference and the first term are -6, 8 respectively and the last term is -82
The arithmetic progression whose first term 26 and common diffrence -7
To find the number of terms in an arithmetic progression (AP), we can use the formula:
nth term (tn) = a + (n - 1)d,
where tn is the nth term of the AP, a is the first term, n is the number of terms, and d is the common difference.
Given that the common difference (d) is -6 and the first term (a) is 8, we can rewrite the formula as:
82 = 8 + (n - 1)(-6).
Simplifying this equation gives us:
82 = 8 - 6(n - 1).
Rearranging the equation further:
82 = 8 - 6n + 6.
Simplifying:
82 = 14 - 6n.
Now, let's isolate "n" by moving the constants to one side and arranging the equation:
6n = 14 - 82.
6n = -68.
Dividing both sides of the equation by 6 gives us:
n = -68/6.
Simplifying this expression gives us:
n = -34/3.
However, since the number of terms cannot be negative or fractional, we conclude that there are no terms in the arithmetic progression.
Thus, the arithmetic progression has 0 terms.
a = -6
d = 8
term(n) = a+(n-1)d
82 = -6 + 8(n-1)
solve for n