Question

Find the sum of the first 37 terms in the sequence 14,23,32,41

Answer 1

6512

Explanation:

This is an arithmetic sequence. Each term is obtained by adding 9 to the previous term.

First term = a = 14

Common difference = d = second term - first term

= 23 - 14

d = 9

number of terms = n = 37

`\boxed{\bf S_n = (n)/(2)(2a + (n-1)d}\\\\\text{\bf $ \bf S_n$ is the sum of first n terms.} \\\\`

`\sf S_(37)= (37)/(2)(2*14 + (37-1)*9)\\\\\\~~~~~ = (37)/(2)(28+36*9)\\\\~~~~~=(37)/(2)*(28+324)\\\\\\~~~~~= (37)/(2)*352\\\\~~~~~= 37 * 176\\\\S_(37)=6512`