Question

The 3rd term of a sequence is 25 and 5th term is 15 . What is its first term? Find the common difference? What is 6th term

Answer 1

ANSWER:

• First term = 35

• Common difference = - 5

• 6th term = 10

GIVEN:

• The 3rd term of a sequence is 25

• The 5th term of a sequence is 15

TO FIND:

• First term

• Common difference

• 6th term

EXPLANATION:

We want to find the common difference. Hence the given term is A.P.

$\bold{ \large{t_n = a + (n-1)d}}\\ \\ \\ \\t_3 = a + (3-1)d\\ \\ \\25 = a + 2d\\ \\ \\t_5= a + (5-1)d\\ \\ \\15 = a + 4d\ \\ \\ \textsf{Subtract the two terms}\\ \\ \\ 25 - 15 = 2d - 4d \\ \\ \\ 10 = -2d\\ \\ \\ d=-5\\ \\ \\ Substitute\:\:d = - 5\:\:in\:\:t_3$

$25 = a + 2(-5)\\ \\ \\ 25 = a - 10 \\ \\ \\ a = 35\\ \\ \\t_6 = a + (5-1)d\\ \\ \\t_6 = 35 + (5)(-5)\\ \\ \\t_6 = 35-25\\ \\ \\ t_6 = 10$

First term = 35

Common difference = - 5

6th term = 10