Question

First term of arithmetic sequence is 7 and its 10 term is 30. a) what is the common difference?.2) write the sequence?. 3) write the algebraic from of the sequence?. 4) write the 50 th term of the sequence?​

Answer 1

Ans:

a). 23/9 = d

Step-by-step explanation:

first term is 7

10th term is 30

a10 = a + (n-1)d

30 = 7 + 9d

30-7 = 9d

23/9 = d

b). a1 = 7

a2 = 7+23/9 = 9.5

a3 = 9.5 + 23/9 = 12

a4 = 12 + 23/9 = 14.5

thus, the sequence is 7,9.5,12,14.5.

d). a = 7 , d = 23/9 , 50th = ?

a50 = 7 + 49*23/9

a50 = 7 + 125.2

a50 = 132.2

Thus, the 50th term is 132.2

Answer 2

Answer:

(a) Common difference:-

first term, a = 7

t10 = a+9d = 34

7+9d = 34

d = 3

common difference , d = 3

(b) 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, ..

(c) The algebraic from of the sequence:-

a, a+d, a+2d, a+3d, ..

7, 10, 13, 16, ..

(d) The 50th term of the sequence:-

t50 = a+(50-1)d

= 7+49(3)

= 7+147

= 154

T50 = 154