Question

if the sum of first three term in AP is42 and that of first five term is 80 find 20 th term of the series

Answer 1

Answer:

Hope it helps you✌

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

★Given -

• Sum of first three terms of an A.P is 42.
• Sum of first five terms of the same A.P is 80.

★To find -

• 20th term of the A.P

★Concept -

• Here, we'll use the formula a(n) = a + (n-1)d to solve the question.

★Solution -

Let the first three terms of the A.P be a - d, a , a + d.

We are given that the sum of first three terms of the A.P is 42.

$\longmapsto \rm{a \cancel{ - d} + a + a + \cancel d = 42}$

$\longmapsto \rm{3a = 42}$

$\longmapsto \rm{a = \dfrac{ \cancel{42}}{ \cancel3} }$

$\longmapsto \rm{ \pink{a = 14} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (1)}$

According to the second statement we know that sum of the first five terms of the A.P is 80.

Now, let the A.P be a ,a + d, a + 2d, a + 3d, a + 4d...

$\boxed{\longmapsto \rm{a + a + d + a + 2d + a + 3d + a + 4d= 80}}$

$\longmapsto \rm{5a + 10d = 80}$

$\longmapsto \rm{5(14)+ 10d = 80 \: \: \: [from \: (1)]}$

$\longmapsto \rm{70 + 10d = 80}$

$\longmapsto \rm{10d = 80 - 70}$

$\longmapsto \rm{10d = 10}$

$\longmapsto \rm{d = \dfrac{ \cancel{10}}{ \cancel{10}} }$

$\longmapsto \rm{ \green{d = 1}}$

$\rm{\therefore a {\tiny20}} = a + 19d$

$\rm{\longmapsto a {\tiny20}} = 14 + 19(1)$

$\rm{\longmapsto a {\tiny20}} = 14 + 19$

$\rm{\longmapsto \orange{ a {\tiny20}}}\orange{ = 33}$

Therefore, the 20th term of the A.P is 33.