Find the number of terms of the A.P. If 1 is added to each term of thi

1.	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.
Answer» The given A.P. is -12, -9, -6,…21 Here, a = -12, d = -9 – (-12) = 3 Let the number of terms be n T_n = 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 = \(\frac{n}{2}\)[2(-11) + (12 -1) x 3] = 6 (-22 + 33) = 66

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.

Answer»

The given A.P. is -12, -9, -6,…21

Here, a = -12, d = -9 – (-12) = 3

Let the number of terms be n

T_n = 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 = \(\frac{n}{2}\)[2(-11) + (12 -1) x 3] = 6 (-22 + 33)

= 66