[[1]] and ____ are the next two terms of an A.P. 4, 9, 14, ….

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Detailed Solution

Given
1st Term T1=4
2nd Term T2=9
3rd Term T3=14
In the given series its first three terms are given and since the given series is in AP so we will first find its common difference for its first three terms
d=T2−T1=9−4=5
d=T3−T2=14−9=5
Hence we can say the common difference of the series is d=5
Now we know the nth term for an Arithmetic Progressive series can be found out by using the formula tn=a+(n−1)d ,where the first term of the series
t1=a=4
Now since we have to find the next two term of the series so the 4th term of the series will be
t4=a+(4−1)d − −(i)
By substituting the values we get
⇒t4=4+3×5 =4+15 =19
And also the fifth term of the series will be equal to
t5=a+(5−1)d − −(ii)
Hence by substituting the values we get
⇒t5=4+4×5 =4+20 =24
So the fifth term of the series is 24
Hence from the above observations we can say the 4th term of the given AP series is 19 and its 5th term is 24.
So the next two terms of the series is 4, 9, 14, 19, 24
So, the correct answer is “4, 9, 14, 19, 24”.

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