Question

consider the Arithmetic sequence 7, 11 , 15, extra
a.What is its 20th term?
b.Find the sum of its first 20 terms.
c.Is the sum of any two terms of this sequence will be a term in this sequence why? ​

Answer 1

The given arithmetic sequence:

7, 11 , 15, ........

Here, first term (a) = 7, common difference (d) = 11 - 7 = 4

We have to find: a) The 20th term of the arithmetic sequence.

b)The sum of first 20th term of the arithmetic sequence,

c) Is the sum of any two terms of this sequence will be a term in this sequence why? ​

Solution:

a) The 20th term of the arithmetic sequence

We know that,

The nth term of the arithmetic sequence,

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

$a_{20}$ = 7 + (20 -1)4

⇒ $a_{20}$ = 7 + 76

⇒ $a_{20}$ = 83

b) The sum of first 20th term of the arithmetic sequence.

We know that,

The sum of first nth term of the arithmetic sequence,

$S_{n}$ = $\dfrac{n}{2}(a+l)$

The sum of first 20th term of the arithmetic sequence,

$S_{20}$ = $\dfrac{20}{2}(7+83)$

⇒ $S_{20}$ = 10 × 90

⇒ $S_{20}$ = 900

c) Yes, the sum of any two terms of this sequence will be a term in the arithmetic sequence.

Thus, a) The 20th term of the arithmetic sequence, $a_{20}$ = 83

b) The sum of first 20th term of the arithmetic sequence, $S_{20}$ = 900

c) Yes, the sum of any two terms of this sequence will be a term in the arithmetic sequence.

Answer 2

Answer:

a)83

b)900

Step-by-step explanation:

Please mark as Brainliest answer and follow me my friend