If the ninety term of an A.P is 30, find the Sum of its first seventeen terms
To find the sum of the first seventeen terms of an arithmetic progression (A.P), we need to know two things: the first term of the A.P and the common difference between consecutive terms.
However, you have given me the 90th term of the A.P instead of the first term. So, we need some additional information to solve this problem.
Could you provide me with either the first term or the common difference of the A.P?
I will assume you meant the ninetieth term.
If a and d are the first term and common difference respectively, then
term(90) = 30
a + 89d = 30
a = 30-89d
sum(17) = (17/2)(2a + 16d)
= (17/2)(2(30-89d) + 16d)
= (17/2)(60 - 162d)