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Formula for Sum of n Terms of an AP

Question 11 W...

Question

Question 11
Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its $54^{t h}$ term?

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Solution

$G i v e n A . P . i s 3, 15, 27, 39, \dots \dots a = 3 d = a_{2} - a_{1} = 15 - 3 = 12 a_{54} = a + (54 - 1) d = 3 + (53) (12) = 3 + 636 = 639 132 + 639 = 771 W e h a v e t o f i n d t h e t e r m o f t h i s A . P . w h i c h i s 771. L e t n^{t h} t e r m b e 771. a_{n} = a + (n - 1) d 771 = 3 + (n - 1) 12 768 = (n - 1) 12 (n - 1) = 64 n = 65 T h e r e f o r e, 65^{t h} t e r m i s 132 m o r e t h a n 54^{t h} t e r m .$

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Similar questions

Which term of the A.P. $3, 15, 27, 39, \dots$ will be $132$ more than its $54^{t h}$ term?

3, 15, 27, 39, . .

132

54 t h

54^{t h}

3, 15, 27, 39, . .

132

54^{t h}

A . P

3, 15, 27, 39, . . . . w i l l b e 132

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