Question

An arithmetic sequence has a common difference of -4 and its 37th term is 10 . Find the first term.

Answer 1

Answer:

154

Step-by-step explanation:

a37=a1+(n-1)d

10=a1+(37-1)-4

10=a1+(36)-4

10=a1-144

10+144= a1

154=a1

Answer 2

The first term of the given sequence is needed.

The first term is $154$

Arithmetic sequence

$d$ = Common difference = $-4$

$a_{37}=10$

An arithmetic sequence is given by

$a_{n}=a+(n-1)d\\\Rightarrow a_{37}=a+(n-1)d\\\Rightarrow 10=a+(37-1)\times-4\\\Rightarrow a=10+36\times 4\\\Rightarrow a=154$

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