# maths

A) In an arithmetic progression the sum of the first ten terms is 50 and the fifth term is three times the second term

(1) Calculate the first term
(2)Calculate the sum of the 20 terms

1. 👍 0
2. 👎 0
3. 👁 95
1. Just translate into Math using the definitions of AP

"the fifth term is three times the second term " ---> a+4d = 3(a+d)
a+4d = 3a+3d
d = 2a **

"the sum of the first ten terms is 50"
--> 5(2a+9d) = 50
2a+9d=10 ***

sub ** into ***
2a+9(2a) = 10
20a=10
a = 1/2
d = 1

first term is 1/2
sum(20)
= 10(2(1/2) + 19(1)) = 200

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### math

The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the

asked by kudu on February 2, 2015
2. ### math

An arithmetic progression as the same first and second terms as the geometric progression. Find the sum of the first 20 terms of the arithmetic progression. How do I do this? I tried to find the common ratio for G.P. and then

asked by lin on September 14, 2016
3. ### maths

the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

asked by festus on March 7, 2012
4. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression

asked by Lucas on February 3, 2013
5. ### math!!

Three numbers are in an arithmetic progression; three other numbers are in a ge- ometric progression. Adding the corresponding terms of these two progressions yields 32, 26, and 32. The sum of the three terms of the arithmetic

asked by Sara V. on May 3, 2017
6. ### AP Calculus

The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p-10, where p is a constant. Given that common difference of the progression is 5, find the value of p.

asked by Watermelon on November 30, 2011
7. ### algebra

if 1, 2, 7 and 20, respectively, are added to the first terms of an arithmetic progression, a geometric progression of four terms is obtained. find the first term and common difference of the arithmetic progression the answers are

asked by Sam on April 27, 2016
8. ### math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G

asked by Stephan on January 2, 2017
9. ### Math

5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression? Note:

asked by Shin on May 11, 2013
10. ### Math (Geometric Progression)

5 distinct positive reals form an arithmetic progression. The 1st, 2nd and 5th term form a geometric progression. If the product of these 5 numbers is 124 4/9, what is the product of the 3 terms of the geometric progression? Note:

asked by Shin on June 22, 2013
11. ### Math

A sequence is called an arithmetic progression of the rst order if the di erences of the successive terms are constant. It is called an arith- metic progression of the second order if the di erences of the successive terms form an

asked by Bhupendra on May 11, 2012

More Similar Questions