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.