Question

find the 7 th term of 1/4,-1/4,3/4,-5/4​

Answer 1

Step-by-step explanation:

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Answer 2

Question:

$Find \: the \: {7}^{th} \: term \: of \: \frac{1}{4}, \: \frac{ - 1}{4}, \: \frac{3}{4}, \: \frac{ - 5}{4}$

Answer:

$\boxed{t_{7} = \frac{ - 11}{4}}$

The given terms are in A.P.

Step-by-step explanation:

$Find \: the \: {7}^{th} \: term \: of \: \frac{1}{4}, \: \frac{ - 1}{4}, \: \frac{3}{4}, \: \frac{ - 5}{4}$

The given terms are in A.P.

$a (first \: term) = \frac{1}{4}$

$d (common \: difference) = t_{2} - t_{1}$

$t _{2} = \frac{ - 1}{4}$

$t _{1} = \frac{1}{4}$

$d = \frac{ - 1}{4} - \frac{1}{4}$

$d = \frac{ - 2}{4}$

$\boxed{d = \frac{ - 1}{2}}$

$t _{n} = a + (n - 1)d$

$To \: find \: the \: {7}^{th} \: term$

$t _{7} = a + 6d$

$t _{7} = \frac{1}{4} + 6( \frac{ - 1}{2})$

$t_{7} = \frac{1}{4} - 3$

$t_{7} = \frac{1 - 12}{4}$

$\boxed{t_{7} = \frac{ - 11}{4}}$

Note:

The formula: tn=a + (n-1)d ,is the formula to find the nth term of an Arithmetic Progression.

Here,

$t _{n} = {n}^{th} term$

$a = (first \: term)$

$n = no.of \: terms$

$d = (common \: difference)$