Question

The 17th term of an Arithmetic sequence is 51. If the commons difference is 7, what is the first term ?

Answer 1

Answer:

The first term is:

• $a_1=-61$

Step-by-step explanation:

The arithmetic sequence is defined by

$a_n=a_1+\left(n-1\right)d$

where

$a_1$ is the first term

$d$ is the common difference

as

the 17th term of an arithmetic sequence is 51.

i.e. $a_{17}=51$

so

$a_n=a_1+\left(n-1\right)d$

$a_{17}=a_1+\left(17-1\right)d$        

$51=a_1+\left(17-1\right)7$         ∵ $n = 17$, $a_{17}=51$ , $d=7$

$a_1+112=51$                   ∵ $\left(17-1\right)\cdot \:\:7=112$

$a_1=-61$

Therefore, the first term is:

• $a_1=-61$