Question

If in ap s6 = 42,s5 = 30. Find the 5th term

Answer 1

Question :-

If in ap s6 = 42,s5 = 30. Find the 5th term

Answer :-

${\pink{\boxed{\underline {Given:- }}}}$

Sum of 6 terms = 42

sum of 5 terms = 30

${\blue{\boxed{\underline{To\:find :-}}}}$

5th term

${\orange {\boxed{\underline{Solution :-}}}}$

s5 = 30

so ,

$\frac{5}{2} (2a + 4d) = 30 \\ 2a + 4d = \frac{30 \times 2}{5} \\ 2a + 4d = 12 ....(1)$

and s6 = 42

so ,

$\frac{6}{2} (2a + 5d) = 42 \\ 2a + 5d= \frac{42}{3} \\ 2a + 5d = 16....(2)$

Subtract (1) from (2)

2a + 5d - 2a - 4d = 16 - 12

d = 4

》 substitute the value of d in equation (1 ) to get a

2a + 4d = 12

2a + 4(4) = 12

2a = 12 - 16

2a = -4

a = -2

we are asked to find the 5th term

5th term = a + 4d = -2 + 4(4) = -2 + 16 = 14

$\huge {\green{\boxed{\underline {5th \: term = 14 }}}}$

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