Question

in an ap the sum of first 4 terms is 20 and the sum of first three terms is 12 find the 4rth term of an arithmetic progression​

Answer 1

Provided Information :-

• The sum of first 4 terms in an ap is 20
• The sum of three terms is 12

To Evaluate :-

• The 4th term of that ap

According to the question :-

Let the first four terms be :-

• a - d
• a
• a + d
• a + 2d

$\\ \sf \qquad \longrightarrow (a - d) + a + (a + d) = 12 \\ \\ \\ \sf \qquad \longrightarrow3a = 12 \\ \\ \\ \sf \qquad \longrightarrow \: a = \cancel \frac{12}{3} = 4$

Now, again, according to the question,

$\\ \sf \qquad \longrightarrow(a - d) + a + (a + d) + (a + 2d) = 20 \\ \\ \\ \sf \qquad \longrightarrow4 + 4 + 4 + 4 + 2d = 20 \\ \\ \\ \sf \qquad \longrightarrow2d = 20 - 16 \\ \\ \\\sf \qquad \longrightarrow \: d = \cancel\frac{4}{2} = 2$

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Answer 2

Answer:

Step-by-step explanation: Sₙ= n/2[2a + (n-1)d]

S₄= 20

Also, S₃= 12

20= 4/2[2a +(4-1)d]

10= 2a + 3d ------ Eqⁿ 1

12= 3/2[2a +(3-1)d]

12/3= a+d

a+d=4

And, a=  4-d-------- Eqⁿ 2

Using 2 in 1, we get

10= 8-2d+3d

d=2

And, a= 4-2=2

So, a₄= 2+(4-1)2

a₄= 2+6

a₄=8

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