SOLUTION: The first term of an arithmetic progression is 6 and the fifth term is 18,find the number of term in the series having a sum of 162

Question 1147514: The first term of an arithmetic progression is 6 and the fifth term is 18,find the number of term in the series having a sum of 162
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Given: 1st term 6; 5th term 18

The difference is 12; the 5th term is 4 terms after the first. So the common difference is 12/4 = 3

With a common difference of 3 and a first term of 6, the formula for the n-th term of the sequence is 3n+3.

The sum of n terms of an arithmetic progression is

(number of terms) times (average of all the terms)

which in an arithmetic progression is

(number of terms) times (average of first and last terms)

We have expressions for all those numbers:
number of terms: n
first term: 6
last (n-th) term: 3n+3

We want to find the number n that makes the sum 162:

Formal algebra or trial and error shows n=9 (the other algebraic solution n=-12 doesn't make sense in the context of the problem).

ANSWER: The number of terms to have a sum of 162 is 9.

CHECK:
1st term: 6
9th term: 6+8*3 = 6+24 = 30
Sum of 9 terms: 9((6+30)/2) = 9(36/2) = 9(18) = 162
RELATED QUESTIONS
The fifth term of an arithmetic progression is three times the second term,and the third... (answered by ikleyn)

The first term of an arithmetic progression is 62 and the fifth term is 74. Find the... (answered by ewatrrr)

The fifth term of an arithmetic progression is three times the second term,and the third... (answered by ikleyn,MathTherapy)

The first term of an arithmetic progression is 12 and the sum of the first 16 terms is... (answered by greenestamps)

A geometric progression has 6 terms. The first term is 192 and the common ratio is 1.5.... (answered by greenestamps)

1.If the third term of of a Geometric Progression is the square of the first and the... (answered by Edwin McCravy)

The fifth term of an arithmetic progression is three times the second term,and the third... (answered by ikleyn)

A geometric progression and an arithmetic progression have the same first term. The... (answered by htmentor)

The 17th term of an arithmetic progression is 81 and the 33th term is 145. Find a and d (answered by plover)