Question

3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.
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Answer 1

Answer:

First term of the sequence is $11$

Step-by-step explanation:

Let $a$ be the first term and $d$ be the common difference

We have

The sum of the second term and the ninth term of an arithmetic sequence is $-5$

$a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1$

The sum of the third and fourth terms of the same sequence is $7$

$a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2$

eqn 1 - eq2

$4d=-12\\\\d=-3$

Substituting in eqn 1

$2a+9\times -3=-5\\\\2a=22\\\\a=11$

First term of the sequence is $11$