Can you help me?? i just dont really know how do it?

Question

what is the first term of an arithmetic sequence with a common difference of -7 and a seventh term of 40??

Answer 1

Common diference of arithmetic sequence d = -7

nth term of a arithmetic sequence a + (n-1)d

a is the first term of a arithmetic sequence

d is the common term of a arithmetic sequence

n is the number of terms

The seventh term of a arithmetic sequence = 40

a + (n-1)d = 40

Substitute n = 7 , d = -7 and a = a

a + (7-1) -7 = 40

a +(6)(-7) = 40

a - 42 = 40

Add 42 to each side

a - 42 + 42 = 40 + 42

a + 0 = 82

a = 82

There fore thew first term of a arithmetic sequence : a = 82.