In an Arithmetic progression:
an = a1 + ( n - 1 ) d
where
a1 = the initial term
an = the nth term
d = the common difference of successive members
In this case:
a9 = a1 + 8 d = 50
a12 = a1 + 11 d = 65
Now you must solve system of two equations:
a1 + 8 d = 50
a1 + 11 d = 65
The solutions are:
a1 = 10 , d = 5
The sum of its first n terms:
Sn = n ( a1 + an ) / 2
In this case:
a70 = a1 + 69 d = 10 + 69 ∙ 5 = 355
n = 70
Sn = n ( a1 + an ) / 2
S70 = 70 ( a1 + a70 ) / 2
S70 = 70 ( 10 + 355 ) / 2 = 12775
The sum of its first n terms also can calculate by formula:
Sn = n [ 2 a1 + ( n - 1 ) d ] / 2
S70 = 70 ( 2 ∙10 + 69 ∙ 5 ) / 2 = 12775
The 9th and 12th term of the A.p are 50and 65 respectivly. Fine (a) the common difference (b) the sum of its first 70 terms
1 answer
1 answer