Question

Find term of an arithmetic sequence is 7 and its 10th term is 34​

Answer 1

Answer:

Consider an arithmetic sequence whose 7th term is 34 and the 15th terms are 66. What is the common difference and what is the 20th term?

To answer this question, we will build two equations with two unknowns, using

a(n) = a(1) + (n-1)d

so,

34 = a(1) + 6d

66 = a(1) +14d

Using elimination by multiply the first term by -1, we get:

-34 = -a(1) -6d

66 = a(1) + 14d

which becomes,

32 = 8d

d = 4

plugging that difference into the first equation, we get

34 = a(1) +6(4)

a(1) = 10

Since we know now know the difference and the first term, we use the first equation is get the 20th term.

a(20) = 10 + (20–1)4

a(20) = 86.

So, the answers to this problem are 4 for the difference, and 86 for the 20th terms

Answer 2

Answer:

Common difference:-

first term, a = 7

t10 = a+9d = 34

7+9d = 34

d = 3

common difference , d = 3

Sequence:-

Sequence - a, a+d, a+2d, a+3d, ..

a = 7,

a+d = 7+3 = 10

a+2d = 7+2(3) = 7+6 = 13

a+3d = 7+3(3) = 7+9 = 16

Sequence:- 7, 10, 13, 16, ..