Saturday

October 25, 2014

October 25, 2014

Posted by **Anonymous** on Thursday, March 1, 2012 at 11:43pm.

- ap -
**Bosnian**, Friday, March 2, 2012 at 1:55amAn arithmetic progression (A.P) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

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

a 1 = first term

In this case:

a 5 = 30

a 1 + ( 5 - 1 ) d = 30

a 1 + 4 d = 30

a 1 = 30 - 4 d

a 12 = 65

a 1 + ( 12 - 1 ) d = 65

a 1 + 11 d = 65

30 - 4 d + 11 d = 65

30 + 7 d = 65

7 d = 65 - 30

7 d = 35 Divide both sides by 7

d = 35 / 7

d = 5

a 1 = 30 - 4 d

a 1 = 30 - 4 * 5

a 1 = 30 - 20

a 1 = 10

The sum S of the first n values of a finite sequence is given by the formula:

S n = ( n / 2 ) * [ 2 a 1 + ( n - 1 ) d ]

In tis case :

a 1 = 10

d = 5

n = 20

S 20 = ( 20 / 2 ) * [ 2 * 10 + ( 20 - 1 ) 5 ]

S 20 = 10 * ( 20 + 19 * 5 )

S 20 = 10 * ( 20 + 95 )

S 20 = 10 * 115

S 20 = 1150

**Answer this Question**

**Related Questions**

arithmetic - in an AP, if the 5th and 12th terms are 30 and 65 respectively. ...

arithmetic - the sum of the 4th and 8th terms is 10, and the sum of the 6th and ...

Math - 1) If the sum of the first n terms of a series is Sn where Sn=2nē-n, (a)...

math - 1) If the sum of the first n terms of a series is Sn where Sn=2nē-n, (a)...

Further mathematics - An exponential sequence (GP)of positive terms and a linear...

Further mathematics - An exponential sequence of positive terms and a linear ...

Geometric - 1) The sum of last three terms of GP having n terms is 1024 time the...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

Math - The first three terms of a GP are also the first,nineth and eleventh ...