math help!
posted by Riana .
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
Respond to this Question
Similar Questions

Maths
1) In the arithmetic progression, the 8th term is twice the 4th term and the 20th term is 40. Find the common difference and the sum of the terms from the 8th to the 20th term inclusive. 2) Find the least number of terms of the AP, … 
MathGr.11 urgent
The 10th term of an arithmetic series is 34, and the sum of the first 20 terms is 710. Determine the 25th term. Can someone please explain how to do this? 
Math
The 10th term of an arithmetic series is 34, and the sum of the first 20 terms is 710. Determine the 25th term. 
arithmetic
given that the first term of an Ap is 7 and its 10th term is twice the second term. calculate the sum of the 28 term. 
math
the 10th term of an arithmetic series is 34, and the sum of the first 20 terms is 710, determine the 25th term. 
arithmetic
the sum of the 3rd and the 4th term is 44 and the sum of the 10th and the 15th term is 203. what is the sum up to the 20th term? 
math
the 10th term is 34 of arithmetic series and the sum of the 20th term is 710.what is the 25th term? 
arithmetic
Determining the first three terms of an ArithmetiC progressionof which the (a.)10th term is 31 and the 15th term is 49 (b.)7th term is 3 and 12th term is 3 (c.)5th term is 8 and the 11th term is 28 (d.)9th term is7+9x and d=2x,Show … 
mathematics
the 10th term of an arithmetic sequence is equal to the sum of 40 and 5th term.If the 15th term is 127 what is its common difference? 
Ap series
Sum of first six term of an ap is 46 ratio of its 10th term to that of 30th term is 1:3. Find its 13th term