if the the fifth time of an ap is 18 and 11th term is 42 the first time is

Answer: The first term is 2.

Step-by-step solution

Step 1: Set up equations using the $n^{\text{th}}$ term formula

Let $a$ be the first term and $d$ be the common difference of the arithmetic progression. Using the formula $a_n = a + (n - 1)d$ , the 5th term is $a_5 = a + (5 - 1)d = a + 4d = 18$ , and the 11th term is $a_{11} = a + (11 - 1)d = a + 10d = 42$ .

Step 2: Solve for the common difference $d$

Subtract equation (1) from equation (2) to eliminate the variable $a$ . This gives $6d = 24$ , which simplifies to $d = 4$ .

Step 3: Substitute $d$ to find the first term $a$

Substitute $d = 4$ back into equation (1). We get $a + 4(4) = 18$ , which simplifies to $a + 16 = 18$ , giving $a = 2$ .

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if the the fifth time of an ap is 18 and 11th term is 42 the first time is

Step-by-step solution

Step 1: Set up equations using the nthn^{\text{th}}nth term formula

Step 2: Solve for the common difference ddd

Step 3: Substitute ddd to find the first term aaa

Step 1: Set up equations using the $n^{\text{th}}$ term formula

Step 2: Solve for the common difference $d$

Step 3: Substitute $d$ to find the first term $a$