First term `a=100`, Common difference `d=5`, Number of terms `n=10`
Find `n^(th)` term (last term) and sum of the arithmetic progression
Solution:
Here first term `a=100,`
Common difference `d=5`
We know that,
`f(n) = a + (n - 1)d`
`f(10)=100 + (10 - 1)(5)`
`=100 + (45)`
`=145`
We know that,
`S_n = n/2 [2a + (n - 1)d]`
`:. S_10 = 10/2 * [2(100) + (10 - 1)(5)]`
`= 5 * [200 + (45)]`
`= 5 * [245]`
`= 1225`
Hence, `10^(th)` term of the given series is `145` and sum of first `10^(th)` term is `1225`
This material is intended as a summary. Use your textbook for detail explanation.
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