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. 👍 1
2. 👎 2
3. 👁 1,125

Isn't the definition of 5th term (a + 4d)
and that of the first term a ?

so a+4d = 6a
4d = 5a
d = 5a/4 -----> **

Also : sum(6) = (6/2)(2a + 5d)
99 = 3(2a + 5(5a/4) )
33 = 2a + 25a/4
times 4
132 = 8a + 25a

continue to solve for a, then sub it back into **

1. 👍 1
2. 👎 1

1. 👍 1
2. 👎 1

Similar Questions

1. sequences and Series

If 5 times the 5th term is equal to the 6 times the 6th term of an arithmetic sequence then its 11th term is.......

2. math

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

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

The first term of an arithmetic sequence is 2.The 12th term in the progression is 9 times bigger than the 2nd term. Find the common difference d.

1. math

The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric

2. 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.

3. mathematics

A goemetric progression is such that the 3rd term is 9times the first term ,while the 2nd term is one-twenty fourth of the 5th term.Find the 4th term

4. 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.

1. Maths

if the sum of the 6th and 7th term of an Arithmetic progression(AP) is 60 and the 3rd term is -5 find the common difference?

2. Math

In an AP, the 9th term is -4 times the 4th term and the sum of the 5th and 7th term is 9. Find the first term and the common difference

3. 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

4. Math

a geometric progression has a third term of 20 and a sum to infinity which is three times the first term. find the first term