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dangina [55]
3 years ago
9

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

Mathematics
1 answer:
Luda [366]3 years ago
7 0
<u>The general formula for an Arithmetic Progression is :</u>

                            \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)}


<u>Equation (2) - Equation (1) :
</u>
13d - 8d = 195 - 120

5d = 75

d = 15


<u>Substitute d = 15 into Equation (1) :
</u>
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) }}


<u>Find 12th term :</u>

T_{12} = 15(12 -1) = 165


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