Finding First Three Terms of an Arithmetic Sequence if Sum of Two terms Given
Hi friend in previous video lesson we learned what happens when the common difference of two arithmetic progressions are same. That was really interesting and tricky too for quickly solving the A.P. problems.
Now in this video we are going to Find First Three Terms of an Arithmetic Sequence if Sum of Two terms Given. Actually here we get some relationships between the terms of the arithmetic progression and solving the relationships we get the value.
So ready to start . I hope pen and notebook is with you.
How was it.
In above problem sum of 4th term and 8th term of Arithmetic progression was 24 and the sum of 6th and 10th term was 44. We need to find the first three terms of the same Arithmetic progression that are 1st term, second term and third term.
How to Solve ?
1. Write all the terms 4th, 8th , 6th and 10th term in terms of first term “a” and common difference “d”.
2. Write first relation as per question i.e. 4th term + 8th term = 24 and solve you will get the vale of first term of arithmetic progression in terms of common difference”d”.
3. Write second relation of the Arithmetic progression as given by question i.e
6th term +10th term = 44
4. Put the value of first term of AP in terms of common difference“d” in the second relation. Solve it you will get the value of common difference “d”.
5. Put the value of d in first or second relation you will get the value of first term of Arithmetic progression.
6. Then second term = first term + common difference
7. Third term = first term + 2(common difference)
I hope you understand how to solve the arithmetic progression problems related to nth term specially finding first terms solving relationships.
Here I have listed few problems based on above problem , solve them you will get the good confidence. If you feel any problem then comment or mail me.
Q1. Which term of an Arithmetic progression 5, 15, 25, …………..will be 130 more than its 31st term? (Ans 44th term)
Q2. The 10th term of an Arithmetic progression is 52 and 16th term is 82 find the 32nd term and the general term. (Ans 32th term = 162, nth term = 5n +2)
Q3. If 10th term of an Arithmetic progression is 52 and 17th term is 20 more than the 13th term find the Arithmetic progression. ( Ans 7, 12, 17, 22, ……….)