Sequence: 10, 21, 32, 43, 54, ... Find the 75th term.

186

Step-by-step explanation:

definition: a_n = a_1 + f * (n-1)

Common difference is 11

The sum of all numbers up through the 17th: 1666

Answer: 824

Step-by-step explanation:

This is problem on progression.

Considering the series / sequence,

10, 21, 32, 43, 54, ...

To find the 75th term, we first of all find which of the sequence is it, is it, Arithmetic or Geometric sequence.

Now fro this, it is an AP sequence because, when the first term us subtracted from the second term and the common difference added to the second term it produces the third term and so on,. Haven't gotten this, we now apply the formula for finding the number if terms in an AP.

Tn = a + (n - 1) d, where n = number of terms we are computing for = 75, a = first term = 10, and d = 21 - 10 = 11.

Now substitute for those values in the formula above

T75 = 10 + (75 - 1) 11

= 10 + 74 * 11

= 10 + 814

= 824.