Question

In an\[AP\], if the common difference \[d = - 4\] and the seventh term \[{a_7}\] is 4, then find the first term.

Answer 1

Hint: Here, we are going to use the formula for the nth term of an AP i.e \[{a_n} = a + (n - 1)d\].

Complete step-by-step answer:
Given, the common difference \[d = - 4\] and the seventh term \[{a_7}\] is 4
We know that \[{a_n} = a + (n - 1)d\]
\[ \Rightarrow {a_7} = a + (7 - 1)( - 4)\]
\[ \Rightarrow 4 = a - 24\]
\[ \Rightarrow a = 28\]
Hence, the first term in the AP is \[a = 28\]
Therefore, \[a = 28\] is the required solution

Note: One should remember the relation between the first term, common difference and the nth term of an AP. If a sequence has negative common difference represents a decreasing arithmetic progression