Q. 394.2( 5 Votes )

Find the number of terms of the AP - 12, - 9, - 6, ..., 21. If 1 is added to each term of this AP then find the sum of all terms of the AP thus obtained.

Answer :

Here, first term = a = - 12

Common difference = d = - 9 - (-12) = 3


Last term is 21.


Now, number of terms in this AP are given as:


21 = a + (n - 1)d


21 = - 12 + (n - 1)3


21 + 12 = 3n - 3


33 + 3 = 3n


36 = 3n


n = 12


If 1 is added to each term, then the new AP will be - 11, - 8, - 5,…, 22.


Here, first term = a = - 11


Common difference = d = - 8 - (-11) = 3


Last term = l = 22.


Number of terms will be the same,


i.e, number of terms = n = 12


Sum of 12 terms of the AP is given by:


S12 = (12/2) × [a + l]


= 6 × [ - 11 + 22]


= 6 × 11


= 66


Sum of 12 terms of the new AP will be 66.


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