Question

sum of the first n terms of an ap is n2+4. find the 15th term of the progression.

Answer 1

Step-by-step explanation:

Given:

$S_n = {n}^{2} + 4 \\ \therefore S_1 = {1}^{2} + 4 =5\\\implies t_1 =5\\</p><p>S_2 = {2}^{2} + 4 =8\\\implies t_2 =8-5=3\\</p><p>\therefore d =t_2- t_1=3-5=-2\\</p><p>\therefore t_{15}= \{5+(15-1)(-2)\}\\</p><p>\implies t_{15}= \{5+14(-2)\}\\</p><p>\implies t_{15}= \{5-28\}\\</p><p>\implies t_{15}= -23$

Thus the 15th term of the given progression is - 23.