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The ninth term of an arithmetic progression is 54 and the sum of the 12 terms 438 find the first term and the common difference?
t(n) = a + 8*d = 54 .. .. .. .. .. .. .. (A)
s(12) = 12*a + 66*d = 438 .. .. .. .. (B)
12*(A) - (B) => 12*A + 96*d -12*A - 66*D = 648 - 438
=> 30*d = 210 = d = 7
Then substituting this value in (A) gives a + 54 = 54 => a = -2
So the first term is -2 and the common difference is 7.
What else can I help you with?
Is 15 26 37 48 59 an arithmetic sequence?
It is an Arithmetic Progression with a constant difference of 11 and first term 15.
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
Arithmetic progression Find the 1st term of the series?
To find the first term of an arithmetic progression (AP), you need at least two pieces of information: the common difference and either the second term or the sum of the first few terms. The first term can be represented as ( a ), and the ( n )-th term can be expressed as ( a_n = a + (n-1)d ), where ( d ) is the common difference. If you know the second term, you can rearrange it to find ( a = a_2 - d ). Without specific values or additional context, the first term cannot be determined.
Which term is the first negative term of the arithmetic progression 242016?
-4 is the first negative term. The progression is 24,20,16,12,8,4,0,-4,...
What is the 14th term in an arithmetic sequence in which the first term is 100 and the common difference is -4?
What is the 14th term in the arithmetic sequence in which the first is 100 and the common difference is -4? a14= a + 13d = 100 + 13(-4) = 48
What is the sum of the first 15 terms of an arithmetic?
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
Is 15 26 37 48 59 an arithmetic sequence?
It is an Arithmetic Progression with a constant difference of 11 and first term 15.
What is the difference between arithmetic progression and geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
What is the difference of arithmetic progression to geometric progression?
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant.That is,Arithmetic progressionU(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1) + d = U(1) + (n-1)*dGeometric progressionU(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1)*r = U(1)*r^(n-1).
What is the first term of an arithmetic sequence with a common difference of 6 and a fifth term of 35?
35 minus 4 differences, ie 4 x 6 so first term is 11 and progression runs 11,17,23,29,35...
Which term is the first negative term of the arithmetic progression 242016?
-4 is the first negative term. The progression is 24,20,16,12,8,4,0,-4,...
What is the 14th term in an arithmetic sequence in which the first term is 100 and the common difference is -4?
What is the 14th term in the arithmetic sequence in which the first is 100 and the common difference is -4? a14= a + 13d = 100 + 13(-4) = 48
What is the common first difference of this arithmetic sequence 65 53 41 29?
16
What is the nth term in the arithmetic sequence?
It is a + 8d where a is the first term and d is the common difference.
The 7th term of an arithmetic progression is 6 The sum of the first 10 terms is 30 Find the 5th term of the progression?
2
Who gave the formula for finding sum of the first 'n' terms in Arithmetic Progression?
RAMANUJANRAMANUJAN
WHAT ARE THE FIRST THREE OF AN ARITHMETIC SEQUENCE WHOSE LAST TERM IS 1 IF THE COMMON DIFFERENCE IS -5?
6
