The term –12, –9, –6, …–21 are in AP. Find the number terms in this AP. Now if 1 is added to each term of this AP. then Find the sum of all the term of the AP thus obtained.

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Detailed Solution

we know that nth term of AP is given by a + (n – 1) d with the help of this formula we can calculate value of n. Now we will form new AP is Added 1 to each term. Now we know that sum of AP is given by the formula.

Hence we can also find the sum of new AP.
Given AP, –12, –9, –6 …21
First term is –12, a = –12
Common difference
d = (–9) – (–12) = 9 + 12 = 3
d = 3
las term tn = 21
nth term is given by
tn = a + (n – 1) d
21 = –12 + (n – 1) 3
21 + 12 = (n – 1) 3

n = 11 +1
n = 12
Hence, there are 12 terms in AP.
Now, let us form a new AP by adding 1 to each term
Hence, we get –11, –8, –5 …22
First (a) = –11
Common difference (d)
d = –8 – (–11)
–8 + 11 = 3
Sun of n terms of AP

⇒ 6 × [–22 + 33]
sn = 6 × 11 = 66
sum of AP of new AP is 65

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