Question

in an ap a=30 d=-6and an=0then find the value of n​

Answer 1

Answer- The above question is from the chapter 'Arithmetic Progressions'.

Concept used: aₙ = a + (n - 1)d

where aₙ = nth term or last term of an AP

a = first term of AP

n = Number of terms of AP

d = Common difference

Given question: In an A.P., a = 30, d = - 6 and aₙ = 0, then find the value of n.

Solution: For an A.P., first term (a) = 30

Common difference (d) = - 6

nth term (aₙ) = 0

We know that aₙ = a + (n - 1)d.

Substituting the values, we get,

0 = 30 + (n - 1)-6

-30 = (n - 1)-6

-30/-6 = n - 1

n - 1 = 5

n = 5 + 1

n = 6

∴ Number of terms (n) = 6.

Answer 2

Answer:

tn=a+(n-1)d

an=30+(n-1)×-6

0=30+(n-1 )×-6

0-30=(n-1)×-6

-30=(n-1)×-6

-30÷(-6)=(n-1)

5=(n-1)

5+1=n

6=n

n=6