Question

The 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively. ​What is the 1st term of the sequence.

Answer 1

Answer:

            a₁ = -1

Step-by-step explanation:

$a_n=a_1+d(n-1)\\\\a_8=a_1+d\cdot7\\\\a_{20}=a_1+d\cdot19\\\\a_{20}-a_8=a_1+19d-(a_1+7d)=12d\\\\56-20=2d\\\\12d=36\\\\d=3\\\\\\ a_1+3\cdot7=20\\\\a_1=20-21=-1$

Answer 2

If the 8th and 20th terms of an arithmetic sequence are 20 and 56 respectively, then the 1st term of the sequence is -1

The nth term of an arithmetic sequence is given by the formula:

$a_n=a+(n-1)d$

The 8th term of the arithmetic sequence is 20

$a_8 = 20\\\\a_8=a+(8-1)d\\\\a+7d=20.......................(1)$

The 20th term of the arithmetic sequence is 56

$a_{20} = 56\\\\a_{20}=a+(20-1)56\\\\a+19d=56.......................(2)$

Subtract equation (1) from equation (2)

12d  =  36

d  =  36/12

d  =  3

Substitute d = 3 into equation (1)

a  +  7d  =  20

a  +  7(3)  =  20

a  +  21  =  20

a   =  20  -  21

a  =  -1

The first term of the arithmetic sequence is -1

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