Question

Find the 12th term of each sequence. a9= 120, a14=195

Answer 1

The general formula for an Arithmetic Progression is :


`\boxed {\boxed {T_n = a_1 + (n-1)d}}`



`\text {Given that } a_9 = 120,`


`T_9 = a_1 + (9 - 1)d = 120`


`a_1 + 8d = 120 \text { ------------------(1)}`



`\text {Given that } a_(14) = 195,`


`T_9 = a_1 + (14 - 1)d = 195`


`a_1 + 13d = 195 \text { ------------------(2)}`


Equation (2) - Equation (1) :


`13d - 8d = 195 - 120`


`5d = 75`


`d = 15`


Substitute d = 15 into Equation (1) :


`a_1 + 8(15) = 120`


`a_1 = 120 - 120`


`a_1 = 0`


`\text {Substitute }a_1 = 0 \text{ and d = } 15,`


`\boxed { \boxed { T_n = 15(n -1) }}`


Find 12th term :


`T_(12) = 15(12 -1) = 165`



`\boxed {\boxed {\text {Answer: The 12th term is 165.}}}`