Find the number of terms of the A.P. If 1 is added to each term of this A.P., then find the sum of all terms of the A.P. thus obtained.

The given A.P. is -12, -9, -6,…21

Here, a = -12, d = -9 – (-12) = 3


Let the number of terms be n


Tn = a + (n – 1) d


21 = -12 + (n – 1) (3)


21 = -15 + 3n


36 = 3n


n = 12


If 1 is added to each term than A.P. is


-11, -8, -5…20


Here, a = -11, d = 3


S12= [2(-11) + (12 -1) * 3]


= 6 (-22 + 33)


= 66


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