## If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term.

By using nth term of an A.P. formulatn = a + (n – 1) dwhere n = number of termsa = first termd = common differencetn = nth termsGiven: t9 = 0⇒ t9 = a + (9 – 1) d⇒ 0 = a + 8d⇒ a = – 8dTo Show: t29 = 2× t19Now,⇒ t29 = a + (29 – 1) d⇒ t29 = a + 28d⇒ t29 = – 8d […]

## Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.

Let the first term be a – dthe second term be athe third term be a + dthe fourth term be a + 2 dGiven sum of consecutive four term is 12⇒ (a – d) + a + (a + d) + (a + 2d) = 12⇒ 4 a + 2d = 12⇒ 2(2 a + d) = […]

## In an A.P. sum of three consecutive terms is 27 and their product is 504 find the terms? (Assume that three consecutive terms in A.P. are a – d, a, a + d.)

Let the first term be a – dthe second term be athe third term be a + dGiven sum of consecutive three term is 27⇒ (a – d) + a + (a + d) = 27⇒ 3 a = 27⇒ a = 27/ 3 = 9Also, given product of three consecutive term is 504⇒ (a – d) × […]

## Sum of first 55 terms in an A.P. is 3300, find its 28th term.

⇒ a + 27d = 60 …… (1)We need to find value of 28th term that is t28Now, by using nth term of an A.P. formulatn = a + (n – 1) dwhere n = number of termsa = first termd = common differencetn = nth termswe can find value of t28 by substituting all the value in formula we get,⇒ t28 = a […]

## Complete the following activity to find the sum of natural numbers from 1 to 140 which are divisible by 4.

The natural number divisible by 4 between 1 to 140 is4, 8, 12, …….136Where first term a = 4Second term t1 = 8Third term t2 = 12Thus, common difference d = t2 – t1 = 12 – 8 = 4tn = 136Now, by using nth term of an A.P. formulatn = a + (n – 1) dwhere n = no. of termsa […]

## In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.

Given t19 = 52 and t38 = 128Now we have to find the value of “a” and “d”Using nth term of an A.P. formula tn = a + (n – 1) dwhere n = no. of termsa = first termd = common differencetn = nth termswe will find value of “a” and “d”Let, t19 = a + (19 – 1) d⇒ 52 = […]

## Find the sum of all even numbers from 1 to 350.

The even natural number between 1 to 350 is2,4, 6, …….348Where first term a = 2Second term t1 = 4Third term t2 = 6Thus, common difference d = t2 – t1 = 6 – 4 = 2tn = 348 (As we have to find the sum of even numbers between 1 and 350 therefore excluding 350)Now, by using nth term of […]

## Find the sum of first 123 even natural numbers.

The first 123 even natural number is2, 4, 6, …….Where first term a = 2Second term t1 = 4Third term t2 = 6Thus, common difference d = t2 – t1 = 6 – 4 = 2n = 123By using sum of nth term of an A.P. is