the 10th term is 34 of arithmetic series and the sum of the 20th term is 710 i.e S20=710.what is the 25th term?
Let a = first term, T1
Let b = Tn+1 - Tn = term difference
a + 9b = 34
S20 = T1 + T2 + ...T19 + T20
= a + (a+b) + (a+2b) + ...(1+19b)
20a + (b)(1+2+3+...19)
= 20 a + 190 b = 710
20a + 180b = 680
10 b = 30
b = 3
a = 34 -27 = 7
Arithmetic Series is
7, 10, 13, 16, 19, 22, 25, 28, 31, 34,...
10th term = 34
Check the sum of the first 20 terms and predict the 25th
I dont understand the question
To find the 25th term of the arithmetic sequence, we need to first find the common difference (d) and the first term (a₁) of the sequence.
We know that the 10th term (a₁₀) is 34, but we don't have enough information to directly find the common difference or the first term. However, we can use the sum of the 20th term (S20) to help us find the common difference.
We have the formula for the sum of an arithmetic series:
Sₙ = (n/2)(a₁ + aₙ)
where Sₙ is the sum of the first n terms of the sequence, a₁ is the first term, aₙ is the nth term, and n is the number of terms.
Using the formula, we can find the sum of the 20th term (S20) by substituting the known values:
710 = (20/2)(a₁ + a₂₀)
710 = 10(a₁ + a₂₀)
Next, we substitute the value of the 10th term (a₁₀ = 34) into the equation:
710 = 10(34 + a₂₀)
710 = 340 + 10a₂₀
10a₂₀ = 710 - 340
10a₂₀ = 370
Now, we can solve for a₂₀:
a₂₀ = 370/10
a₂₀ = 37
Now that we have the common difference (d) and the first term (a₁₀), we can use them to find the 25th term (a₂₅):
a₂₅ = a₁₀ + (25 - 10)d
a₂₅ = 34 + 15d
Since we don't have the exact value of the common difference (d), we cannot find the 25th term (a₂₅) without additional information.