10th term of an arithmetic sequence is 30 and 20th term is 70 .find the common difference,and it's first term and also the sequence
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Answered by
4
Answer:
20th term - 10th term = 70 - 30
10 = 40
then, 1 = 40/10 = 4
The difference = 4
10th term = 30
30 ÷ 4
Quotient = 7 and remainder = 2
10th term = [ 4 × ( 10 - 3 ) ] + 2
=> [ 4 × 7 ] + 2
=> 28 + 2 = 30
it means the pattern of the number is
4 × ( term - 3 ) + 2
then, the first term
=> [ 4 × ( 1 - 3 ) ] + 2
=> [ 4 × (-2) ] + 2 )
=> (-8) + 2
=> -6
I hope it's help you please mark me as brainlist.
Answered by
0
as given
10th term of an AP is 30
and 20th term is 70
a10=30
a20=70
a10=a+9d eq 1
a20=a+19d eq2
eq2-eq1
substitute the values of a10 and a20 in both eq
a+19d=70
a+9d=30
then,
a+19d=70
-a-9d=-30
by simplifying we get
10d=40
d=40 divided by 10
d =4
substitute d=4 in eq 1
we get
a+9d=30
a+9×4=30
a+36=30
a= 30-36
a= -6
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