Answer:
Least number of terms of A.P will be 10.
Step-by-step explanation:
we know that first term of A.P , a = 3
second term of A.P , b = 8
Now to calculate difference d between first and second term = (8-3) = 5
Let n be the number of terms whose sum is 250 .
Now we know that sum of A.P (Sₙ) is given by
Sₙ = [tex]\frac{n}{2}[/tex] [ 2a + (n-1) d]
substituting values of Sₙ, a and d in above equation we get
250 = [tex]\frac{n}{2}[/tex] [ 2 × 3 + (n-1) 5]
500 = 6n + 5n² -5n
taking equations on one side
5n² + n -500 = 0
now we know that number of terms cannot be a negative number so we will use quadrati formula
n= [tex]\frac{-b }{2a}[/tex] ±[tex]\frac{\sqrt{b^{2}-4ac }}{2a}[/tex]
where a =5 and c = -400 and b =1
n = [tex]\frac{-1+100.4}{10}[/tex]
so n = [tex]\frac{99.4}{10}[/tex]
since n is the number of term so it can only be a whole number so n will be equal to 10.
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