Question

If the 7th term of an ap is 1/15 and the 12th term is 1/25,find the 20th term?
WITH FULL EXPLINATION?

Answer 1

$a {\tiny{20}} = \large \frac{ - 1}{375}$

Step-by-step explanation:

Given -

• 7th term of an A.P is 1/15.
• 12th term of the A.P IS 1/25.

To find -

• The 20th term of the A.P .

Solution -

$\large a \tiny{7} = \large\frac{1}{15}$

$\mapsto a + 6d = \large\frac{1}{15} \: \: \: \: \: \: \: \: \: \: \: (i)$

$\large a \tiny{12} = \large\frac{1}{25}$

$\mapsto a + 11d = \large\frac{1}{25} \: \: \: \: \: \: \: \: \: (ii)$

(i) - (ii),

$a + 6d \: - (a + 11d)= \large\frac{1}{15} - \frac{1}{25}$

$\mapsto \cancel{a} + 6d \: \cancel{- a} - 11d= \large\frac{1 \times 5 - 1 \times 3}{75}$

$\mapsto - 5d= \large\frac{5 - 3}{75}$

$\mapsto - 5d= \large\frac{2}{75}$

$\mapsto d= \large\frac{2}{75 \times ( - 5)}$

$\mapsto d= \large\frac{2}{ - 375}$

$\mapsto d= \large\frac{ - 2}{ 375} \: \: \: \: \: \: \: \: \: \normalsize(putting \: \: in \: (i))$

$\mapsto a + 6( \frac{ - 2}{375}) = \large\frac{1}{15}$

$\mapsto a - \frac{ 12}{375} = \large\frac{1}{15}$

$\mapsto a = \large \frac{1}{15} + \frac{12}{375}$

$\mapsto a = \large \frac{1 \times 375 + 12 \times 15}{15 \times 375}$

$\mapsto a = \large \frac{375 + 180}{15 \times 375}$

$\mapsto a = \large \frac{ \cancel{555}}{ \cancel{15} \times 375}$

$\mapsto a = \large \frac{ 37}{ 375}$

$Now, \: a {\tiny{20}} = a \: + 19d$

$\mapsto a {\tiny{20}} = \large \frac{37}{375} \: + \small{19} \large\frac{ - 2}{375}$

$\mapsto a {\tiny{20}} = \large \frac{37}{375} \: + \large\frac{ 19 \times ( - 2)}{375}$

$\mapsto a {\tiny{20}} = \large \frac{37}{375} \: + \large\frac{ - 38}{375}$

$\mapsto a {\tiny{20}} = \large \frac{ - 1}{375}$

Answer 2

$a {\tiny{20}} = \large \frac{ - 1}{375}$

Step-by-step explanation:

a20 = -1/375