Question

Third term of an a.p is 15 and sum of its 10 terms is 125 . Find 10th term and sum of first n terms

Answer 1

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Answer 2

Concept:

Arithmetic Progression: It means the sequence of number in which the common difference is constant.

Common Difference: It is the difference between the two consecutive terms of a sequence. It is denoted by "d".

First term of the AP is denoted by "a" and the number of terms in an AP is denoted by "n". The sum of an AP with "n" terms is denoted by "S(n)".

Given:

We are given that:

a3=15

S(10)=125.

Find:

We need to find:

a10 and S(n)

Solution:

First, we will see the third term:

a3=a+2d=15

a=15-2d

Now,

S(10)=10/2(2a+(10-1)d)

S(10)=5(2[15-2d]+9d)

125=5(30-4d+9d)

25=30+5d

5d=-5

d=-1

Putting this value to find a:

a=15-2(-1)

a=17

a10=a+9d

a10=17-9

a10=8.

Sum of the n terms:

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

S(n)=n/2(34+(n-1)(-1))

S(n)=n/2(35-n)

S(n)=(35n-n²)/2.

Therefore, we get that the 10th term is 8 and the sum of first n terms is (35n-n²)/2.

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