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Alika [10]
3 years ago
13

Find a1 and d for an arithmetic sequence with these terms. a3=-8 and a7=32

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0
We know that
the formula for the <span>arithmetic sequence is
</span><span>an = a1 + (n - 1)*d
where
a1  is the first term
n is the numbers of terms

for n=3   a3=-8
-8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1

for n=7   a7=32
-32=a1+(7-1)*d----> -32=a1+6*d----> equation 2

multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3

add equation 1 and equation 3
</span>-8=a1+2*d
32=-a1-6*d
----------------
24=-4*d------> d=-6
-8=a1+2*(-6)    (substitute the value of d in equation 1)
-8=a1-12-----> a1=-8+12-----> a1=4

the answer is
a1=4
d=-6

<span>

</span>
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