Question

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If the last term of an Ap is -49,and the 1st term is 3 ,and d is -2,how many terms are in the AP when the 45th of an Ap is 30

Answer 1

Given: a = 3, d = -2, term(45) = 30
check:
a + 44d = 30
a - 88 = 30
a = 118
contradiction !!! the question is bogus

checking further ....
if last term is -49
a + (n-1)d = -49
3 + (n-1)(-2) = -49
-2n + 2 = -52
-2n = -54
n = 27

There would be 27 terms, the bot claimed there were 16
actually the bot got n = 16.5, which would have been nonsense, since
the number of terms must be a whole number

Answer 2

Given:
aₙ = -49
a₁ = 3
d = -2

We need to find n when aₙ₊₄₅ = 30

We can use the formula for the nth term of an AP:
aₙ = a₁ + (n - 1)d

Substituting the given values:
30 = 3 + (n - 1)(-2)
30 = 3 - 2n + 2
2n = 33
n = 16.5

Since n must be a whole number, the 45th term of the AP is when n = 16.
Therefore, there are 16 terms in the AP.