The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

5

Step-by-step explanation:

The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 1st term

We know we have an arithmetic sequence.

a_n = (n - 1) * d + a_1

given:

a_6 = 35 = (6-1) * d + a_1

a_13 = (13 - 1) * d + a_1 = 77

find a_1

we have 35 = 5d + a_1

and 77 = 12d + a_1

2 equations in 2 unknowns.

We can solve this.

77 = 12d + a_1

35 = 5d + a_1

minus the 2 equations from each other.

77 - 35 = 12d - 5d + a_1 - a_1

42 = 7d

d = 6

Find a_1

35 = 5*6 + a_1

35 = 30 + a_1

a_1 = 35 - 30 = 5

a_1 = 5