Question

find the 6 th term of AP 7,11,15,19,... find the sum of first 6 terms

Answer 1

ANSWER:

Sixth term = 27

Sum of first six terms is 102

GIVEN:

7,11,15,19,... are in A.P

TO FIND:

$\textsf{ 6^{th} term and sum of 6 terms}$

FORMULAE:

$d = t_2 - t_1 \\ \\ A_n = a + (n - 1)d \\ \\ S_n = \frac{n}{2}\bigg(2a + \big(n - 1\big)d\bigg)$

EXPLANATION:

a = 7

d = 11 - 7

d = 4

$A_6 = 7 + (6 - 1)4\\ \\A_6 = 7 + 5(4)\\ \\A_6 = 7 + 20\\ \\A_6 = 27\\ \\ \\ S_6 = \frac{6}{2}\bigg(2(7) + \big(6 - 1\big)4\bigg)\\ \\ S_6 = 3\bigg(14 + 5(4)\bigg)\\ \\ S_6 = 3(14 + 20)\\ \\ S_6 = 3(34)\\ \\ S_6 = 102$

Sixth term = 27

Sum of first six terms = 102