Answer:
Option (4)
Step-by-step explanation:
Given sequence is,
-3 + 6 + 15 + 24 + ........+ 132
Difference in 1st and 2nd term = 6 - (-3)
= 9
Difference in 2nd and 3rd term = 15 - 6
= 9
There is a common difference of 9 in each successive term.
Therefore, it's an arithmetic sequence.
Let the nth term of this sequence is (a + bn).
For the first term → n = 0,
a = -3
For second term → n = 1
-3 + b(1) = 6
b = 6 + 3
b = 9
Therefore, nth term of the sequence will be,
[tex]T_n[/tex] = -3 + 9n
For nth term = 132
-3 + 9n = 132
9n = 135
n = [tex]\frac{135}{9}[/tex]
n = 15
Sum of 15 terms can be represented by the expression;
[tex]\sum_{n=0}^{15}(-3+9n)[/tex]
Option (4) is the answer.