# 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.

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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