The sum of the first six terms oa an AP is 42.the ratio fo the 10th term to 30th term of an ap is 1/3.calculate the first term and the 13th term.

# The sum of the first six terms oa an AP is 42.the ratio fo the 10th term

Let a be the first term and d be the common difference

Sum of 6 terms = S_{6} = (6/2) [ 2a + 5d ] = 42 or 2a+5d = 14 …(1)

from eqn.(1), if we substitute a = d, then we get a = 2

13th term = 2+12(2) = 26