Question

an ap consists of 37 terms the sum the of the first 3 terms of it is 12 and the sum of its last 3 term is 318 the find the first and last term of the progression ​

Answer 1

SOLUTION

GIVEN

An AP consists of 37 terms the sum the of the first 3 terms of it is 12 and the sum of its last 3 term is 318

TO DETERMINE

The first and last term of the progression

EVALUATION

Let a be the First term and d be the Common Difference

So first three terms are a , a + d , a + 2d

∴ a + a + d + a + 2d = 12

$\implies \sf{3a + 3d = 12}$

$\implies \sf{a + d = 4} \: \: \: - - - - (1)$

Again last three terms are

a + 36d , a + 35d , a + 34d

So by the given condition

a + 36d + a + 35d + a + 34d = 318

$\implies \sf{3a + 105d = 318}$

$\implies \sf{a + 35d = 106} \: \: \: - - - (2)$

Equation 2 - Equation 1 gives

34d = 102

$\sf{ \implies \: d = 3}$

Again equation 1 gives

a = 4 - 3 = 1

FINAL ANSWER

First term = 1 & Common Difference = 3

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