The 13th term of an A.p. is 39 and The 23rd term is 69. find The 18th term of This A.P.
Answers
Answer:-
18th term of A.P. = 54
Step-by-step explanation:
Given, 13th term = 39 and 23th term = 69.
a + 12d = 39
a + 22d = 69.
From the above two equations, we can deduce, we get d = 3.
−10d = −30
d = 3. [subtracting both equations]
Substituting 'd' = 3 in either equation, will give 'a'.
a + 12d = 39
a + 12(3) =39
a + 36 = 39
a = 39-36
a = 3
First term 'a' = 3.
t18 = a + 17d
t18 = 3 + 17(3)
t18 = 54.
18th term of the A.P. = 54.
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Given,
13th term of an AP = 39
23rd term of the AP = 69
To find,
The 18th term of the AP.
Solution,
We can easily solve this problem by following the given steps.
According to the question,
We have:
13th term of an AP = 39
23rd term of the AP = 69
We know that the following formula is used to find the nth term of an AP:
an = a+(n-1)d where a is the first term, n is the number of the term and d is the common difference
a13 = 39
a+(13-1)d = 39
a+12d = 39 ---(1)
Now, we have:
a23 = 69
a+(23-1)d = 69
a+22d = 69 ---(2)
Now, subtracting equation 1 from equation 2,
a+22d-a-12d = 69-39
10d = 30
d = 30/10 (10 was in the multiplication on the left-hand side. So, it is in the division on the right-hand side.)
d = 3
Putting the value of d in equation 1,
a+12d = 39
a+12(3) = 39
a+36 = 39
a = 39-36
a = 3
So,
a18 = a+(18-1)d
a18 = a+17d
Putting the value of a and d,
a18 = 3+17(3)
a18 = 3+51
a18 = 54
Hence, the 18th term of the AP is 54.