Question

In an arithmetic progression, the sixth term is equal to 10.5; and the difference is 1.5. Find the first term and the sum of the first 9 terms.

Answer 1

The first term will be 3 and the sum of the first 9 terms will be 81.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Given,

Six terms as 10.5

So,

a₆ = 10.5

Common difference(d) = 1.5

The nth term of an AP is given by

$a_{n}$ = a + (n-1)d

So,

a₆ = a + (6-1)d

10.5 = a + 5(1.5)

a = 3

Now,

The Sum of n terms is given by

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

S = 9/2[6 + 8(1.5)]

S = 81

Hence the first term will be 3 and the sum of 9 terms will be 81.

For more about Arithmetic progression

brainly.com/question/20385181

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