Question

consider the arithmetic sequence 6,14,22
a)what is its 7th terms?
b)what is the sum of its 13 terms of this sequence?

Answer 1

Answer:

a=112

b=__________________

Answer 2

Answer:

The arithmetic sequence formula is used for the calculation of the nth term of an arithmetic progression.

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

The sum of n terms when nth term is unknown can be found using the formula.

Sn = n/2[2a + (n − 1)d]

Given:

Arithmetic sequence 6, 14, 22 …26 terms.

⇒ a = 6

d = 14 - 6 = 8

⇒ n = 26

Now by substituting these values on the formula, we get

S26 = 26/2 [2(6) + (26−1)8]

By further calculation, we get

S26 = 13[12 + (25)8]

So we get,

S26 = 13[12 + 200]

S26 = 13[212]

S26 = 2756

Therefore, the sum of the arithmetic sequence is 2756.

What is the sum of the arithmetic sequence 6, 14, 22 …, if there are 26 terms?

Summary:

The sum of the arithmetic sequence 6, 14, 22 …, if there are 26 terms is 2756.