Question

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

Answers

Bosnian
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







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