Question

find the first term and common difference of the arithmetic described.
7th term is 7, 22nd term is 52 what is the first term?

Answer 1

a + 6d = 7 where a = first term and d=common difference
a + 21d = 52 (22nd term)

solve this system of equations and you have it.

Answer 2

i suggest you subtract the first equation from the second - this will eliminate a

Answer 3

not sure how i plug this in

Answer 4

a + 21d = 52
a + 6d = 7
-------- subtract:
15d = 45

so now you can find what d is right?

Answer 5

3

Answer 6

?

Answer 7

yes d = common difference = 3
now plug d=3 into the first equation so as to find the value of the first term a.

Answer 8

21*3=63

Answer 9

?

a + 6d = 7
so
a +6(3) = 7

a = 7 -18

a = ?

Answer 10

-11

Answer 11

yup

Answer 12

now i need to find an-1+?

Answer 13

i got that i just need to know an?

Answer 14

?
we have now found the common difference = 3
and first term which is -11

Answer 15

so what is an?

Answer 16

an - that the nth term right?

Answer 17

ya

Answer 18

if so
it is a +(n-1)d = -11 + 3(n -1)

Answer 19

= 3n - 14

Answer 20

so thats the formula than?

Answer 21

yep - that s the formula for the nth term (an) of this series