Question

Write the sum using summation notation, assuming the suggested pattern continues. -3+6+15+24+...+132

Answer 1

Option (4)

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,

`T_n` = -3 + 9n

For nth term = 132

-3 + 9n = 132

9n = 135

n =
`(135)/(9)`

n = 15

Sum of 15 terms can be represented by the expression;

`\sum_(n=0)^(15)(-3+9n)`

Option (4) is the answer.