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How many terms are there in an arithmitic progression the sum of whose terms is 820 if the first term is 3 and the common difference is 4?
sum_ap = n(2a + (n-1)d)/2
→ 2sum = n(2a + (n-1)d)
→ 2sum = 2an + dn² - dn
→ dn² +(2a - d)n - 2sum = 0
a = 3 (first term)
d = 4 (common difference)
sum = 820
→ 4n² + (2×3 - 4)n - 2 × 820 = 0
→ 4n² + 2n - 2 × 820 = 0
→ 2n² + n - 820 = 0
→ (2n + 41)(n - 20) = 0
As n must be positive, the (2n + 41) gives a negative value for n so cannot be a solution, leaving
n - 20 = 0
→ n = 20
There are 20 terms in the AP.
What else can I help you with?
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 }.
What is the sum of series of arithmetic progression having a common difference of 3.5.If the first term is 0.5 and the last term is 25?
sum = 1/2 x number_of_terms x (first + last) number_of_terms = (last - first) ÷ difference + 1 = (25 - 0.5) ÷ 3.5 + 1 = 8 ⇒ sum = 1/2 x 8 x (0.5 + 25) = 102
What is the difference between HCF and GCF?
No difference. In this context, highest and greatest mean the same thing.
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
What is the pattern of 150 175 200?
The pattern in the sequence 150, 175, 200 is an arithmetic progression with a common difference of 25. Each term is obtained by adding 25 to the previous term. This can be represented by the formula for an arithmetic sequence: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the position of the term in the sequence, and (d) is the common difference.
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 }.
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 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...
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 sum of series of arithmetic progression having a common difference of 3.5.If the first term is 0.5 and the last term is 25?
sum = 1/2 x number_of_terms x (first + last) number_of_terms = (last - first) ÷ difference + 1 = (25 - 0.5) ÷ 3.5 + 1 = 8 ⇒ sum = 1/2 x 8 x (0.5 + 25) = 102
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 most common harmonic progression for the Blues?
The C major chord is the chord that you will learn when first learning music.
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,...
In an arithmetic progression six times the sixteenth term?
If a is the first term and r the common difference, then the nth term is tn = a * (n-1)r So t16 = a + 15r Then 6*t16 = 6(a + 15r) or 6a + 90r No further simplifiaction is possible.
In AP if the 6th and 13th terms are 35 and70 respectively find the sum of its first 20 terms?
To find the sum of the first 20 terms of an arithmetic progression (AP), we need to first determine the common difference (d) between the terms. Given that the 6th term is 35 and the 13th term is 70, we can calculate d by subtracting the 6th term from the 13th term and dividing by the number of terms between them: (70 - 35) / (13 - 6) = 5. The formula to find the sum of the first n terms of an AP is Sn = n/2 [2a + (n-1)d], where a is the first term. Plugging in the values for a (the 1st term), d (common difference), and n (20 terms), we can calculate the sum of the first 20 terms.
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 is the difference between HCF and GCF?
No difference. In this context, highest and greatest mean the same thing.
