Question

write the next four terms of ap a-b,a+b,a-3b

Answer 1

Question:

Write the next four terms of ap $a-b,a+b,a-3b$.

To find:

★ To find next four terms.

Answer:

The next four terms are $\underline{ \sf \pink{\bold{ a-5b,a-7b,a-9b,a-11b}}}$

Given:

★ Three consecutive terms are given, which is in A.P.

Step-by-step explanation:

$a-b,a+b,a-3b$

Above consecutive terms are in A.P.

$\star \: First \: term \: \underline{ (a) = a - b }$

$\star \:Common \: difference \: \underline{ (d) = t_{2} - t _{1}}$

✴️ $\: t _{1} = a - b$

✴️ $\: t _{2} = a + b$

$\hookrightarrow d = (a + b) - (a - b)$

$\hookrightarrow d = \bold{a} + b \bold{- a } + b$

$\hookrightarrow \boxed{d = 2 b}$

$\star \:Common \: difference \: \underline{ (d) = 2b}$

General term of A.P.

$a,a + d,a + 2d,a + 3d,.....etc$

Here, First term $t_{1}= a=a-b$

Second term $t_{2}= a+d=a+b$

Third term $t_{3}= a+2d=a-3b$

Now finding the next four terms ;

Fourth term $t_{4}= a+3d$

Fifth term $t_{5}= a+4d$

Sixth term $t_{6}= a+5d$

Seventh term $t_{7}= a+6d$

Now substituting the values,

✨$\: t_{4}= a + 3d = a - b + 3(2b)$

$\rightsquigarrow \boxed{t_{4}= a + 3d = a - 5b}$

✨$\: t_{5}= a + 4d = a - b + 4(2b)$

$\rightsquigarrow \boxed{t_{5}= a + 4d = a -7b}$

✨$\: t_{6}=a + 5d = a - b + 5(2b)$

$\rightsquigarrow \boxed{ t_{6}=a + 5d = a - 9b}$

✨$\: t_{7}=a + 6d = a - b + 6(2b)$

$\rightsquigarrow \boxed{ t_{7}=a + 6d = a-11b}$

$\therefore$The next four terms are $\underline{\bold{ a-5b,a-7b,a-8b,a-11b}}$

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More information:

Arithmetic Progression :-

In a sequence the difference between two consecutive terms are equal it is called Arithmetic Progression .

General form :-

$a,a + d,a + 2d,a + 3d,.....etc$

$\bold{{n}^{th}\:term}$ :-

$t _{n} = a + (n - 1)d$

No. of terms :-

$n = \dfrac{l - a}{d} + 1$

Answer 2

Answer:

n. = l-a/d - 1

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