#### 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.

Find the first term of the sequence.

Find the 5th term of the sequence.

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