Question

the sixth term of an ap is 80 and its fifteenth term is 16 percent.find the first three terms of the ap​

Answer 1

Given that:

The 6th term of an AP is equal to four times its first term and the sum of first six terms is 75

Let us assume first term = a

Common difference = d

Number of terms = n

According to given condition:

a6 = 4a ———- (1)

We know that a 6 =a + 5d ———-(2)

Substituting eq (2) in (1) we get

a + 5d =4a

3a = 5d

a= 5d / 3 ————-(3)

Sn= n / 2 X [2a + (n-1) d]

So substituting the given data and values from above equation we get

75 = 6 / 2 X [2* 5d/3 + (6-1) d]

75= 3[ 10d/3 + 5d]

75=3(25d/3)

75= 25d

d=3

Substituting the value of d in eq (3)

We get,

a= 5d / 3

a= 5(3)/3

a=5

Therefore, the first term a = 5 and d = 3

Given: The 6th term of an AP is equal to four times its first term and the sum of first six terms is 75

Let a is the first term and d is the common difference and n is the number of terms

Now

Now

a= 5 and d= 3

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Now

a= 5 and d= 3