In an AP , if the 10th term of an AP is 81 and the sum of first 10 terms is 120 find the n term
Answers
Hello !!
We have a aarithmetic progression that the 10th term is 81 and the sum of your first 10 terms is 120. If you make a good interpretation about it, you have that the formula to you solve it is.
Sn = (n/2) × (Ak + An)
Now, you put the information of the statement in the formula and develop.
120 = (10/2) × (Ak + An)
[...] The 10th term is 81 [...]
[...] The sum of the 10th terms. [...]
Therefore, only with this information we have the conclusion that the number of terms of this arithmetic progression is 10.
I hope I have collaborated !
Answer:
a^18 = 81
a+17d=81 ..............eq(i)
S^10 = n/2[2a+(n-1)d]
120=10/2[2a+(10-1)d]
120=5[2a+9d]
120/5=2a+9d
24=2a+9d ...........eq(ii)
By elimaniting equation (i) and (ii) we have
[a+17d =81] ×2
[2a+9d=24]
2a+34d=162
-2a+9d=24
-___-__-_____
0+25d= 138
d=138/25 =5.52
now put the value of d=138/25 in eq (i) a+17d=81
a+17 × 138/25=81
a+17=81×25/138
a+17=14.67
a= -2.32
now nth term is
a^n=a+(n-1)d
a^n= -2.32+(n-1)5.5.2
a^n =-2.32+5.52n-5.52
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