Question

the first term of an arithmetic sequence is 6.the sum of first six terms is 66.what is its sixth term?​

Answer 1

Answer:

Required 6th term of this AP is 16.

Step-by-step explanation:

Here,

First term of an AP = 6

Sum of first six terms = 66

From the properties of APs :

• Sum of n terms = n / 2 x [ a + l ] , where a is the first term and l represents the last term of that AP.

Thus, in this question :

= > Sum of 6 terms = 66

= > 6 / 2 x [ 6 + last term( sixth term ) ] = 66

= > 3[ 6 + sixth term ] = 66

= > 6 + sixth term = 66 / 3

= > 6 + sixth term = 22

= > sixth term = 22 - 6

= > sixth term = 16

Hence the required 6th term of this AP is 16.

Answer 2

Answer:

Step-by-step explanation:

Given :-

First term of an AP = 6

Sum of first six terms = 66

To Find :-

Sixth term.

Formula to be used :-

n/2x[a + l]

Solution:-

From the properties of APs :

Sum of n terms = n/2x[a + l]

According to the question,

⇒  Sum of 6 terms = 66

⇒  6/2x [ 6 + last term( sixth term ) ] = 66

⇒ 3[ 6 + sixth term ] = 66

⇒  6 + sixth term = 66/3

⇒  6 + sixth term = 22

⇒  sixth term = 22 - 6

⇒  sixth term = 16

Hence the required 6th term of this AP is 16.