Question
It is given that the common difference of an arithmetic sequence is 7, and the sum of the 3rd term and the 6th term is 23.
Find the first term of the sequence.
Find the 5th term of the sequence.
Answer
According to the formula for the general terms of an arithmetic sequence
a_3= a_1+2d
a_6 = a_1+5d
Using the given condition a_3+a_6 = 23 and d = 7
a_1+2d+a_1+5d = 23
solve the function
a_1=\dfrac{23-7\times 7 }{2} =-13
a_5 = a_1 +4d
=-13+4\times 7
=15
Therfore, the 5th term of the sequence is 15