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# Find the sum of the first 22 terms of an AP in which d = 7 and 22^{nd} term is 149

**Solution:**

Sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d].

Here, a is the first term, d is the common difference and n is the number of terms.

Given,

- 22
^{nd}term, l = a₂₂ = 149 - Common difference, d = 7

We know that nth term of AP, aₙ = a + (n - 1)d

a₂₂ = a + (22 - 1) d

149 = a + 21 × 7

149 = a + 147

a = 2

The sum of 22 terms can be found as follows.

Sₙ = n/2 [a + l]

= 22/2 (2 + 149)

= 11 × 151

= 1661

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 5

**Video Solution:**

## Find the sum of the first 22 terms of an AP in which d = 7 and 22^{nd} term is 149

Class 10 Maths NCERT Solutions Chapter 5 Exercise 5.3 Question 7

**Summary:**

The sum of the first 22 terms of an AP in which d = 7 and 22^{nd} term is 149 is 1661.

**☛ Related Questions:**

- Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
- If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
- Show that a1, a2,... , an , ...form an AP where an is defined as below (i) an = 3 + 4n (ii) an = 9 - 5n. Also find the sum of the first 15 terms in each case.
- If the sum of the first n terms of an AP is 4n - n2, what is the first term (that is S1)? What is the sum of the first two terms? What is the second term? Similarly find the 3rd,the 10th and the nth terms.

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