The first term and the common difference of the Arithmetic Progression which the given sum of the first 5 terms are respectively; 6 and 1/4
We are told;
Sum of first 5 terms of the AP = 65/2
Formula for sum of n terms of an AP is;
S = ⁿ/₂(2a + (n - 1)d)
65/2 = ⁵/₂(2a + 4d)
⇒ 65 = 5(2a + 4d)
13 = 2a + 4d ------(1)
Formula for the nth term of an AP is;
aₙ = a + (n - 1)d
five times the 7th term is the same as six times the second term.
7th term is; a₇ = a + 6d
second term is; a₂ = a + d
Thus;
5(a + 6d) = 6(a + d)
5a + 30d = 6a + 6d
a = 24d
Put 24d for a in eq 1 to get;
13 = 2(24d) + 4d
13 = 52d
d = 13/52
d = ¹/₄
Thus; a = 24(¹/₄) = 6
Read more about Arithmetic Sequence at; https://brainly.com/question/6561461
