Question

In an AP a=2 and sum of the first five terms is one-fourth the sum of the nexifire terms.Show that its 20 th term is -12 .



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Answer 1

Step-by-step explanation:

Given :-

• first term = a = 2

• sum of the first five terms is one-fourth

• 20 th term is -12 .

Sum of n terms is Sn = 1/2[( 2a +(n-1)d]

Let the common difference be d.

The sum of first five terms is one-fourth of the next five terms.

• S5 = 1/4(S10-S5)

=> (5a + 10d) = 1/4(5a + 35d)

=> 20a + 40d = 5a + 35d

=> 15a + 5d = 0

=> 3a +d = 0

=> d = -3a = -6

The 20th term = a + (20–1)d

• = a + 19d
• = 2 + (19×(-6))
• = 2 - 114
• = -112.

Hence proved !