The 1st term of an AP is 6 and the 5th term is 18.find the number of term in the series having a sum of 162?
d = (18-6)/4 = 3
n/2 (2*6 + 3(n-1)) = 162
n = 9
N=9
9
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The 4th term of an AP is 6.if the sum of the 5th term is 18.find the number of term in the series hearing a sum of 162.
Well, well, well, let's put on our thinking caps and solve this! To find the number of terms in the series, we need to know the common difference. Any ideas what it might be?
To find the number of terms in the arithmetic progression (AP) that has a sum of 162, we need to determine the common difference (d) and the nth term (aₙ) of the AP.
Given:
First term (a₁) = 6
Fifth term (a₅) = 18
We can use the formula for the nth term in an AP to find the common difference:
a₅ = a₁ + (5 - 1)d
18 = 6 + 4d
12 = 4d
d = 12/4
d = 3
Now that we have the common difference (d = 3), we can find the nth term using the following formula:
aₙ = a₁ + (n - 1)d
Substituting the known values, we can find the nth term when the sum is 162:
162 = 6 + (n - 1)3
Simplifying the equation:
162 = 6 + 3n - 3
162 - 6 = 3n - 3
156 = 3n - 3
3n = 156 + 3
3n = 159
n = 159/3
n = 53
Therefore, the number of terms in the series that have a sum of 162 is 53.