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Question
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Solution
In this problem, we are given an A.P. and we need to find a30 - a10.
A.P. is 4,9,14,19 .....
Here,
First term (a) = 4
Common difference of the A.P. (d) = 9 -4
= 5
Now, as we know,
an = a + (n- 1) d
Here, we find a30 and a20.
So, for 30th term,
a30 = a + (30 - 1 ) d
= 4 + (29)(5)
= 4 + 145
= 149
Also, for 10th term,
a20 = a +(10-1) d
= 4 + (9 ) (5)
= 4 + 45
= 49
So,
a30 - a10 = 149 - 49
= 100
Therefore, for the given A.P a30 - a10 = 100 .
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