# Mathematics

If the sixth term of an arithmetic progression (A.P) is 37 and the sum of the six term is 147, find the first term, common difference, sum of the first fifteen terms

1. 👍 0
2. 👎 0
3. 👁 111
1. Just use the formulas you know. You have only learned a few rules so far, so the problems will have to use the few you already have.

a + 5d = 37
6/2 (2a+5d) = 147
so, a=12, d=5, and
S15 = 15/2 (2*12 + 14*5) = 705

1. 👍 0
2. 👎 0
👨‍🏫
oobleck
2. In an arithmetic progression nth term:

an = a1 + ( n - 1 ) d

a1= initial term

d = common difference

a6 = a1 + ( 6 - 1 ) d = 37

a1 + 5 d = 37

Sum of n terms in A.P:

Sn = n ∙ [ 2 a1 + ( n - 1) ∙ d ] / 2

In this case n = 6

S6 = 6 ∙ [ 2 a1 + ( 6 - 1) ∙ d ] / 2 = 147

3 ∙ [ 2 a1 + 5 d ] = 147

6 a1 + 15 d = 147

Now you have system of two equations:

a1 + 5 d = 37

6 a1 + 15 d = 147
___________

Try to solve it.

The solutons are:

a1 = 12 , d = 5

Sum of the first fifteen terms:

Sn = n ∙ [ 2 a1 + ( n - 1) ∙ d ] / 2

S15 = 15 ∙ [ 2 ∙ 12 + ( 15 - 1) ∙ 5 ] / 2

S15 = 15 ∙ [ 24 + 14 ∙ 5 ] / 2

S15 = 15 ∙ ( 24 + 70 ) / 2

S15 = 15 ∙ 94 / 2

S15 = 1410 / 2

S15 = 705

Check of results.

12 , 17 , 22 , 27 , 32 , 37 , 42 , 47 , 52 , 57 , 62 , 67 , 72 , 77 , 82

Sum of first 6 terms in:

S6 = 12 + 17 + 22 + 27 + 32 + 37 = 147

S15 = 12 + 17 + 22 + 27 + 32 + 37 + 42 + 47 + 52 + 57 + 62 + 67 + 72 + 77 + 82 = 705

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

the ninth term of an arithmetic progression is 52ind the and the sum of the first twelve terms is 414.find the first term and the common difference.

2. ### kite

the sixth term of an arithmetic progression is 21 and the sum of the first 17 terms is 0. write the first three terms.

3. ### math

If 6 times the sixth term of an arithmetic progression is equal to 9 times the 9th term, find the 15th term.

4. ### Math

In an arithmetic progression, the 5th term is six times the 1st term and the sum of the first six terms is 99. Find the 1st term and the common difference. Attempt at solution: U5 = 6(U1) 99 = 3(2[U1] + 2d)

1. ### arithmetic progression

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference.

2. ### Mathematics

If the sixth term of an A.P is 37 and the sum of the first sixth term is 147.find the first term and the sum of the first 15 terms

3. ### AP calculus

The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

4. ### Maths

A Geometric progression X has a first term of 4a and its sixth term is 256. Another Geometric progression Y has a first term of 3a and its fifth term is 48. Find the: (i) First term of X (ii) Sum of the first four terms of X

1. ### math

if the sixth term of an arithmetic progression is 37 and sum of the first six term is 147

2. ### 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

3. ### maths

the sum of first 8 terms of an arithmetic progression is 156.the ratio of its 12th term to its 68th term is 1:5.calculate the first term and the fifteenth term. please help this questions please.

4. ### Maths

The 5th term of an arithmetic progression is 3times of 2nd term and 12th term exceeds 2times of 6th term by 1. Find the 16th term